This has to be one of the weirdest question I've heard!
Are you actually afraid that owning a cute animal will make you less manly? Out family dog is a Shih Tzu mixed with a Pomeranian. The result is 4 and a half pound of pure cuteness (and evil). My father, who by no means could be considered "girly" love that dog as much as anyone in the house and never questioned his manliness while relating to it (well, maybe a few times just to kid around, but that I'm pretty sure it's not the issue here.). Actually, my father is my dog's favorite master (every dog has one)! I have noticed, however, that in order to keep his "manliness" about the dog, my father likes to refer to him as "4 ans a half pound of muscle".
Personally, I think "cute" stuff doesn't mean that only girls can like it. It would be as if saying that any man keeping a garden is "girly", which couldn't be farther from truth. And just as Janet said, a cute dog is a girl magnet, so someone would have to be pretty dumb to think that simply because you relate to something cute, you are somehow less of a man.