¿Esto suena natural? I made a bad gaffe. I didn't know my boss wears a wig.

"I made a huge gaffe. I didn't know my boss wore a wig."

Gaffes are always "bad" so to emphasize you should say "big", "huge", or maybe even "awful".

I chose "wore" here because it seems more natural in this context. It seems weird to use a non-past verb when the main verb is a "perceptive" verb, since it wouldn't be possible for you to know a "present" condition in the past anyway.

Compare: "I didn't know you lived in this neighboorhood!" or "I didn't know you drank coffee!". Even if the action still happens now, you would use the past tense for "perception" verbs, I think.