OP - I've also had this conversation with my partner who is having his stag do soon. You aren't alone, you aren't a prude, you aren't abnormally distrusting. My reasoning is different to yours, but that's neither here nor there.
I did get worked up about this ages ago, and ended up with a huge ball of resentment festering, but after we talked about it, I felt so much calmer. Part of it is just knowing that you have given them your expectations. That's all you can do. The rest is up to him to show you the kind of person he is.
If my partner ended up going to a strip club with his friends, I would lose a shit ton of respect for him, and said so. It's not even fucking original. It's ridiculously expensive with table charges, and the drinks are £12 for 90% water. Likewise, if he gets offered a private dance by his mates, it's his decision whether or not to have it. That would cross from loss of respect territory to active disgust though. It was his choice if he said anything to his friends in advance, or chose not to, or whatever, but he is a grown man, and his behaviour is his responsibility.
He decided to say something privately to his friends. It's come up...three times since then, and never in a "hurrr hurrrr ALL THE STRIPPERS way". One guy said "I heard about the ground rules" and I simply said "Cool". A girl mentioned that the guys had been talking about "the ground rules" and I said "Yeah? They are good people, and I trust them not to deliberately cause an argument between us". That's it.
Really your problem here is his dickish mates. They are probably enjoying your cowed, panicked reactions. Why don't you give them a proverbial kick in the balls to take the wind out of their sails?
Next time they raise it, look them calmly in the eye and say:
"I have known you guys for years, and I trust you enough not to deliberately do something which would call the wedding into question"
or
"I know you are good friend's of my partner, and believe that you won't put him in any situations where he has to choose between losing face and losing my trust. That's not what friends do".
or
"Well if that's the extent of your originality when planning a stag do, then I pity you"
or
"If that really is the case, then I certainly hope that your hotel and travel tickets don't have any cancellation charges".
They are being pillocks. Show them by being calm and controlled, but reacting.
(For me, paying money to a woman for a sexual service (and being paid to get naked and dance around/on someone IS a sexual service) is foul. It's a pathetic power trip which treats women and women's bodies like chattel).