I don't think so. Several women have, thankfully, found me attractive even though I have little hair left on my head. One of them was even willing to marry me last year.
"Hairless" means more than that. I am not hairless: I have a (short) beard and some hair on my arms, legs, and assorted other body parts that need not be listed here. I am, however, considered bald - though not totally bald (a third term you might add to this list), since I still have a fringe of hair around the sides and back of my head.
If you call someone bald they might get offended, but I don't think it's a problem with the word. I think if a person's sensitive about the fact that they're bald, then they'd be offended about the fact that someone's pointing it out, not because they're using the wrong terminology. So I don't think there's anything wrong with the word "bald" for just a general usage or when referring to people comfortable with being bald, it's a pretty neutral term.
I don't think "hairless" would be a good word to apply to humans, generally. It's a word more often applied to animals, e.g. hairless rats or hairless cats. And as Egmont pointed out, being partially or completely bald on the top of your head doesn't mean you necessarily completely lack hair.
I think if Russia had an equivalent of Michael Jordan (see the picture in the link below), then they might not be so negative about it. Certainly in the 50s, 60s, 70s and 80s, baldness was a dreaded phenomna for most American men.
I think, in large part, that Michael Jordan changed that forever in the USA. Other countries are lagging behind in that matter.