Maybe some of the modern game controllers could fit, I know some of them have mic jacks but I don't know if any have built microphones. They fit the bill for handheld trackpad/etc with plenty of buttons at least.

Yes, but its gonna be weird. I've done very tangentially related work with game controllers, and my suspicion is you're gonna have to try a few (dozen?) before you find one that even sends reasonable commands. I can imagine a FireTV stick sending game controller inputs. I have no idea, but that's the type of thing that might go wrong.

A MX3 air mouse might be the exact thing you want though.

I was looking into this when I got sick and couldn't type anymore. There are some corporate presentation tools that have directional buttons and also mics. I think Microsoft presenter is one? In the end i just ended up using my phone.