"open mike" vs. "open mic"

Solution 1:

Mike is a noun informally used to mean microphone; it is a term used in both British and American English. Mic is a short for microphone.

Looking at the Corpus of Contemporary American English, there are 119 sentences containing "open mike," and 48 sentences containing "open mic."

Solution 2:

Clearly you've given it a lot of thought, and I don't think there is going to be an argument that will sway you. Merriam-Webster says that both are correct, and classifies them both as nouns (rather than abbreviations). It says mike is older, and has a separate entry for open mike. So you can feel completely comfortable and justified using mike, though you will have a hard time convincing mic fans that mic is wrong, particularly with both being endorsed by a reputable authority. I suspect mic is gaining in popularity relative to mike.

Personally, I prefer mic because (as noted by Malvolio and Hostile Fork) there is less chance for ambiguity or misunderstanding.