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.