Yes, the "socket-saver" or "hub saver" or "plastic pipe reamer" tools work.
As with all tools, there are better and worse ones, and generally the better ones cost more. I would see if you can rent a good one from a tool rental place rather than spend a lot on a tool you will probably only use once; or spending not much on something from the folks that sell cheap stuff that looks vaguely like it will work but actually ends up costing you more because it doesn't cut properly, isn't the right size, etc. and generally doesn't actually work.
Hmm. I think there's a prior question where there are pictures of various versions. Let me see...here we go. As noted there, the cost of a good one you'll only use once may well be less than having a plumber come by to do that part, if you could even get a plumber to come by and do just that part. But rental would be preferable.
As for 2" shower drain .vs. maintaining 1-1/2" grandfathered, I tend to think that there's a good reason they changed code, when they bother to change code, so it's preferable to follow current code when you can, even if the inspectors would let you use the grandfathered size. 1-1/2" pipe has 56% of the hole that 2" pipe does (that r-squared factor for area of a circle...)