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.

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.

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.

Windows 11 has a "voice access" application that is amazing, seemingly hidden, and much better than the other built-in Win voice svcs. Voice Access is fully local, poorly documented, and the advanced settings menu is hidden.

*Quick guide to save you time:

-you can say "scroll to top/bottom", "click ok", "open Firefox", etc.

-it will always be typing when you talk unless it a) hears a command, b) you say "command mode", which will listen only for commands, or c) you mute:

-"mute" puts mic to sleep so you don't accidentally type when speaking ("unmute" to unmute)

-say "what can I say" to open advanced menu, allowing you to setup custom voice commands ("open projects folder", "open xyz website", etc.). Works well!

-full voice control of mouse is possible but a little slow. "Open grid" splits screen into a numbered 3x3 grid. You pick a number, it creates a new 3x3 grid in side the box you chose, and repeat until you can tell it to click.

The other thing I tried on Android is Futo voice input via F-droid + an app that turns you phone into a bluetooth keyboard (so as I spoke, it "typed" on the target device). The keyboard app is "Bluetooth Keyboard & Mouse"). It worked smoothly sometimes and other times not.

They make trackball clickers[1] (often with a laser since they're for presentations), and other single handed devices, a search for "finger mouse" surfaces a few different devices

I don't know if any of them have PTT with microphone but you should be able to pair the clicker with a regular bluetooth headset, while the headset may be on all the time you might be able to use something like joy-2-key and a macro/hotkey utility to map the button press to mic mute.

[1] https://www.amazon.com/Wireless-Handheld-Finger-Trackball-Po...

It sounds like you want a dictation mic. Philips’s SpeechMike and OM System’s (formerly Olympus) RecMic are big in the healthcare space. My SpeechMike is wireless with a USB dongle and has something akin to a trackpoint for mouse movement, and buttons that can be programmed to send keystrokes.

Dictation mics are not cheap, unfortunately, but you may be able to get used ones for much less.