I wouldn't expect MIDI to be a good fit, and when I experimented with it a few years ago I wasn't able to get anything I liked. Pitch and volume are continuous, and while this can be encoded in MIDI it's awkward. If you send too many updates you can overwhelm the synth, and if you slide a single note too far it will re-trigger the note. Also when the sound starts you know "there's whistling" before you have a great estimate of the pitch, but MIDI wants to know the initial tone (and many voices have tuned onsets).

But if you want to try it, checking out https://github.com/jeffkaufman/whistle-synth and asking Claude or Codex to add MIDI support would probably work!