I think that asking to know about a woman before he sleeps with her so you can give your two cents is perfectly reasonable and not too limiting at all. After all, you share your body with this man on a regular basis, if he unknowingly sleeps with someone who's hiding disease or drama up her sleeve it will badly affect you!
As for your concern about people thinking he's cheating on you, why don't you accompany him to the bar a few times and make your approval clear, like come over and kiss him on the cheek while he's chatting up a girl, wink at her, tell her he's a catch and say "I'm heading home now to skype with my girlfriend but you two have a wonderful evening, k?" Then grin at him and say "text me if you're staying out late, handsome."
That would send the message to the town loud and clear, but also might be a liiittle more out and proud than you're ready to be?