Which Song Was This (new wave 80's)?

I would say it was Bronski Beat's "Smalltown Boy". Although Culture Club's "Do You Really Want To Hurt Me" was also filmed at a swimming pool (or part of it, anyway), Boy George didn't look like a "white skinny guy" - and he sounded like a black woman!! Jimmy Sommerville, lead singer for Bronski Beat, fits your description (even though some would say his high-pitched vocal makes him sound like a girl, too). So I think you're thinking of "Smalltown Boy". Hope this helps.