Or you could just have sex anyway:
Towel, condom, and with the lights off...
And if the guy is that 'scurred'.... you could blind fold him while you lead him to the shower...
Eventually, a guy's going to realize a woman has a period... and either he will want sex at that time or he won't.
As for a guy being picky about you mentioning that you are on your cycle... the only reason he should be picky would be if you announced that to him in a public environment.
"Hey honey, I'm on the rag! Just wanted you to know," may not go over well in front of his friends or while you're eating. However, there should be no problem informing him in the comfort of your own home... or when you pull him off to the side away from everyone else.
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen