It's definitely the "pee" sound that turns me off Peter, also.
And I've noticed that when this name comes up, I'm the only one who thinks of the fact that "peter" is a slang term for penis. Maybe it's an old-fashioned term that isn't used much any longer, but I always think of it. Motivated by curiosity, I just Googled "Peter as a slang term" and pulled up a website called Slang City which lists names that have another meaning as a slang term and then judges how bad the name is. It says that Peter is not bad because the slang term is secondary to the name. Then again, it also says that Colin is "bad" because it can be pronounced with a long O, the way that Colin Powell does, and this means "the large intestine." I think that's a dumb thing to say because most Colins don't pronounce it that way and I can't see that making Colin a bad name. My nephew's name is Colin, not pronounced with a long O, and he doesn't have any problem with it. So I'm going to discount what this site says about Peter.
Well, even so, it does seem that I'm the only one who makes the association of Peter and penis.