If size is an issue, it seems like you’re going to need to use surface-mounted components to fit the sensor and microcontroller along with supporting electronics, in which case I don’t think you’ll get much smaller than an accelerometer IC:
It’s more than you need, but it’s quite small (6mm x 6mm x 1.5 mm QFN) and you can buy a single unit from digikey for $3.18. That seems pretty small and cheap, but the catch is that it’ll be difficult to solder, which is why people typically purchase them on breakout boards, and it’s a 3.3V part.
A switch made from a spring would also work, but I don’t know of any prebuilt solutions (I’m not saying there aren’t any out there, just that I can’t help you with finding them) and I think making your own could be a bit difficult mainly because you’d need to finely calibrate the mechanics for it to work. There isn’t going to be much difference between the forces it experiences from natural arm swings and the forces it experiences as you shake your wrist more violently. At least an accelerometer would let you do the calibration in software. Also, I could easily see a homemade solution being bigger than an accelerometer IC, but it would be much easier to solder and might prove more satisfying to you.