Music theory

This is a question for any music nuts/jazz improvising nuts like me on this forum. I have an question. If you're playing and improvising over a C major chord progression and you run into C major's relative B half-diminished chord, would you want to use a C or a C# over that chord? You would modally play a C natural over your B locrian scale, whose diatonic 7 chord would be a Bø, but over a Bø by itself, you would play a C# since you would just play a B minor scale with a diminished 5th. Sorry for all the mumbo-jumbo, but this is confusing me.

I say punt.

I really like jazz but the nature of jazz is very mechanical. There is a mathematical clarity in jazz. It's a clean form of music.

Jazz is actually unclean to most classically trained listeners and players. It has a certain dissonance to it at times which is not displeasing to the ear, but artistic.