You don't need a breaker. You need a disconnect switch.
You can just fit one of those, and call it a day.
However in most cases, the cheapest way to get a disconnect switch is to get a panel with a main breaker, since breakers are also switches. You don't care about the breaker part. You could add other functionality, like, say, GFCI, to this main breaker; you might care about that.
Or... you can usually retrofit a main breaker
Now, many novices fitting a panel go "1, 2, 3 breakers, therefore I'll buy a 4-space panel" or sometimes a 2-space panel with a tandem breaker. Then they enjoy the money savings of ... a latté. We're not fans of lattés around here, because we know how often users come back saying "My panel is full. How do I add space?" That problem is very easily avoided, so we shout from the rooftops the message of "think BIG" on panels.
Now if you didn't "think big", this probably won't help. But most panels 12 space or larger are built with space, busing and knockouts reserved for dropping in a field retrofitted main breaker, typically in a different form-factor than the regular breakers, and bolting up where the main lugs go. The panel instructions will discuss this.
If that's the case, then you just do that.
If your panel is too small to be one of those, then heed our advice on "think big" and maybe take it back and get one that is. At that point you should shop for one that includes a main breaker and maybe is bundled with some bonus breakers in a combo-pack. Some of these even throw in AFCI or GFCI breakers. If you're extra clever, get the same panel series as your house, so you can use the bonus breakers in your house.
Or... you can backfeed a breaker
This doesn't work on anything but plain breakers. Breakers are AC, and don't actually care which direction the power flows. (i.e. which side is the power plant and which is the load). So it's possible to fit a 2-pole breaker in a branch-circuit location and backfeed it, making this the panel's "main" breaker.
The backfeed breaker must be tied down, using a UL-listed "tie-down kit" provided by the panel maker.
The panel instructions may specify certain locations a backfeed breaker must be in. However, by convention, you want it at the top, and visually distinct -- obviously separated from the other breakers somewhat. For instance on a 2-column-wide panel, I will generally not put any breakers opposite (to the right of) the main breaker. (this may be a requirement due to stab limits, for 100A+ breakers).
I would never use the inside breakers on a quadplex to backfeed. So if the panel is that strained for space, it's time to take it back and get an 18-space panel.
Backfeed may be your best play for very small 4-8 space panels. But of course that consumes two full spaces of your precious few! (see? Spaces get gobbled up!)
I want the nearby breaker to trip first
That's called selective coordination. Overcurrent-wise, it ain't gonna happen. Not least, your main panel's breaker will be a branch circuit breaker, and your subpanel's breaker may be a main breaker. They have different trip curves, and the news ain't good there. Now let's talk about the 3 types of trip.
Bolted fault, massive overcurrent: Magnetic trip. In this case, fuggedaboutit. It'll be a dog's breakfast which one trips.
Modest overload (thermal trip): Now first, let me stop you. If this happens often enough to care about, that means you under-specced your feeder cable. Don't do that. But now, trip curves come into play. The main panel's branch circuit breaker is more likely to trip than your subpanel's main breaker, because of different trip curves.
Now suppose you back-fed. Both the main panel's breaker and the subpanel's "main" will be in the same category, so it'll boil down to manufacturing tolerances which goes first. If you were extra-clever and your subpanel is the same panel family as the main panel (e.g. both BRyant/Eaton BR), the breaker may be the same model number. In that case, you could pay attention and see which one tends to trip first, and if needed, swap them. The two breakers see exactly the same amount of current. But again, if modest overloads happen often enough to collect this data, your feeder is too small. Fix that.
GFCI. Oh boy, oh boy, oh boy. GFCI. Yeah. Having it trip locally is worthwhile. Right now, you put the GFCI at the main panel instead of at the subpanel. That is better in one way: it protects the feeder cable run from ground faults. But it's bad in the way you care about: local reset. Further, a GFCI trip will knock out the lights in the shed, so you'll be groping around in the dark trying to find the umbrella.
Most people regard GFCI-protecting the feeder itself as not particularly worthwhile. So you might dump that. Abolish the GFCI breaker in the main, and have it at the sub, either as multiple branch circuit breakers, deadfronts or receps, or as a "main breaker".
How to get a GFCI (local) main breaker
How do you get a GFCI "main breaker" for a panel? Not easily. Let's wind back to your original question, which is that you need a disconnect switch because your subpanel does not have a main breaker. You can add on a "hot tub subpanel" for scarcely more than the cost of a bare GFCI breaker, and simply use that as a disconnect switch.
"But I already bought this $80 GFCI breaker that will go in my main panel!" Right, you can't backfeed a GFCI breaker. Easy, though. Look at the breaker itself; say it says "Eaton BR". Go get an "Eaton BR" 2-space main-lug subpanel. Feeder goes to the input lugs, and come off the GFCI's 3 terminals to go to the subpanel proper. Mind you, this requires a 4-wire feed from the panel; if you have a 3-wire feeder, you must not tie neutral and ground past the GFCI, or you will utterly defeat its protection and kill somebody.
By the way, "don't mix breaker types" is not brand loyalty; it's compatibility. The bus stabs are not the same, and the wrong ones will arc. UL has a scheme for cross-listing breakers where appropriate. It's usually not.