When I first started idly thinking about this, I wasn't yet at the point of wanting something wireless.

I thought I might get one of those keyswitch testers and modify it to act like a tiny keyboard. That would be a lot of work and would probably look like a porcupine with lots of wires and things hanging off of it. I'm glad I didn't pursue that very much, because....

There are plenty of off-the-shelf and DIY "stream decks" for use with OBS Studio and other applications. Those are like small keyboards with 3, 5, 15, or however many buttons to which you can assign functions. Most of the interesting ones will let you assign custom keys or sequences of keys to any button so you can make them do your bidding. They cost only a few bucks (or many bucks if you are so inclined) and look like they are really well-made, but they connect over a USB cable. That rules them out for my (evolved) purposes. I might someday get one or two of these and take them apart to see if I could easily do something about replacing the guts to make them wireless.

Here are a few, not including custom-made stream decks featured on Hackaday or Instructables.