Bad news: given a typical portable generator, you'd have the wrong switch for the job
While your intentions with the transfer switch you are looking at are noble, your plans, like many well-intended but underinformed generator transfer setups, would not normally quite reach the point of Code compliance. In particular, while your plan treats the hots correctly (the most important part for not zapping linesmen), your proposed setup would run aground where neutral and ground meet if you used it with a garden-variety portable generator. In particular, your main panel has the neutral-to-ground bond in it, which is a critical component of your house's electrical system. However, most generators also have a neutral-to-ground bond in them, as well, so that they can be safely and legally used as stand-alone power sources, say on a jobsite or somewhere else utility power is unavailable.
As a result, if you hooked up everything as you are currently planning it with a typical generator, you'd have a case of dueling neutral-to-ground bonds, sending stray currents in undesired directions and possibly even tripping the GFCIs protecting the high-power outlets on some generators. There are two ways to fix this: one is to pull the bond out of the generator, but this renders it unusable for portable work, and very few generator manufacturers these days provide instructions for removing and reinstalling the bonding straps on their products. The other, normally less problematic way is to get a transfer switch that switches both the hots and the neutral. This way, your house wiring is only connected to one neutral-ground bond at any given time, whether it be the house's or the generator's.
In particular, your current proposal uses a GE TC10324R double-throw, non-fusible enclosed switch with two switching poles and a solid neutral. However, if you had a bonded neutral generator, you would need a three pole switch in order to have enough poles to switch everything. GE makes one of these, the TC35324R, but it's unobtanium for us DIYers. However, Midwest makes a not-quite-equivalent switch known as the GS3262G, which is somewhat available. Furthermore, Siemens makes a full equivalent to the TC35324R in the DTNF324R (HD has it on their site, even, but it's a bit spendy).
Worse news: you're a switch would have been even more wrong for the job at hand
If we were not switching an entire house, or switching a feeder from a combination meter breaker device, we would be done here. However, since you are transferring your entire house, and likely have your main breaker fitted at your main panel instead of at your meter, we're not done here, as there are more hurdles to overcome. In particular, NEC 230.91 requires the service overcurrent protection to be in the same spot as the service disconnect:
230.91 Location. The service overcurrent device shall be an
integral part of the service disconnecting means or shall be
located immediately adjacent thereto. Where fuses are used as
the service overcurrent device, the disconnecting means shall
be located ahead of the supply side of the fuses.
This leaves you with two options if you wanted to continue down this path with a typical portable generator: either a made-for-purpose, service entrance rated, 200A manual transfer switch with a switched neutral fitted, or a fused double-throw, three-pole safety switch. This poses a problem, as the former switches generally don't have switched neutrals, and the latter are extremely expensive. (Generac discontinued the switched neutral kit for their version, and the EZ-Connect switches don't even seem to offer the option to begin with.)
Even if you could get such a switch for a reasonable price, you'd still find yourself in an installation pickle, as the aforementioned neutral-to-ground bond for your house would have to be moved from your existing main panel to the new switch. This requires replacing the service-entrance cable between the two locations with a four-wire cable, at a minimum; you may also need to extend the grounding electrode conductor to the location of the new panel, which is a challenging task as you need to use compression splices and their associated tooling for this job.
There's a better solution to the problem of standby power out there
Of course, none of this solves the problem of load-management. While it's possible to do that by manually flipping breakers on and off in your panel, there's a reason that you don't see whole-building transfer in larger buildings: it doesn't scale as load-management concerns start to predominate. Manual load selection is error-prone in the heat of a power outage, and even automatic load shed devices can pose problems if they misoperate or are misconfigured.
Instead, what people whose generators actually matter do is take the time up-front to determine which loads and circuits are important enough to belong on the generator, then move those loads to a subpanel that is switched between the normal and standby power sources. This approach means that non-critical loads (like the dryer) can't disrupt critical loads (like the well pump), at the cost of not being able to have the dryer, in this example, on generator power at all. It also means that you can use a smaller, less-expensive transfer switch, and don't have to worry about relocating the service disconnect and its associated neutral-to-ground bond to the transfer switch, for that matter.
The simplest way to do this for most generators, albeit not yours, would be to use an integrated switching neutral manual transfer switch and standby subpanel; Reliance Controls makes such a thing in the form of their Panel/Link X series, and certain Eaton CHGEN panels have this feature as well. (It's also possible to kit out certain main-lug QO panels as such a thing, but it takes a bit more work.) If none of the aforementioned are an option, one could use a three-pole, double throw, non-fused switch and an ordinary main lug subpanel instead.
Fortunately, with your generator, since it has a floating neutral, you can dispense with some of that complexity, and use a more normal manual transfer switch with a solid neutral, or even a pair of interlocked breakers in a bog-standard subpanel with the standby loads fed from that new subpanel.
Of course, you'll need to provide a four-wire feed from the main panel to the transfer switch, with neutral and ground separated and the neutral/ground bond removed/not fitted at the subpanel. This approach also generally lends itself better to using a separate inlet box and transfer switch, instead of having the inlet mounted into a knockout on the transfer switch (or a generator cord and plug trailing from the transfer switch) as in your proposal.
Good news: If you really want to do whole-house manual transfer...things are actually rather simple
If, for some reason or another, the use of a standby subpanel is absolutely not an option for you, it is possible to do whole-house transfer in your situation. The good news is that you can get made-for-purpose hardware for this; the bad news is that what you have won't quite do the trick, due to the NEC 230.91 compliance issue mentioned above.
For your case, the simplest route, instead of using a separate transfer switch, would be to get the correct breaker interlock kit for your electrical panel (in your case, a HOMCGK2C), and use that to interlock the main breaker with the generator breaker. You can then run normal house wiring from the generator breaker to a generator inlet box (Reliance PB50 or equivalent) mounted on the outside of the house; from there, the generator just plugs in using a generator cordset (NEMA 14-50R to CS6364).
If you were trying to do this with a bonded neutral generator, you'd need a 200A enclosed circuit breaker device in a weatherprooof (NEMA 3R) enclosure to serve as the new exterior service disconnecting means. This goes next to your meter enclosure, with a normal 3-wire set of service-entrance wires run into it and the grounding electrode conductor extended/rerun to it as well. From there, though, you then need to run a four-wire feeder to one of the aforementioned 200A three-pole, double-throw switches (either a GS3262G, most likely, or the DTNF324R if you must), with a generator inlet fitted directly to the switch using a Reliance Controls PK50 kit. (A cord-and-plug setup for connecting the generator could be set up using the correct cord grip where it joins the permanent wiring, but some inspectors may consider such a "generator tail" outside the scope of what cordage can legally be used for.) Finally, you would need to continue that four-wire feeder run from the transfer switch to the existing interior panel, removing the bonding means at that panel while you're at it since it's now going to be a subpanel.
