Yeh, in fact, it's more common than most people realize. I've known guys, mainly athletic types, who shaved their legs and arms. People either assume that they have baby thin blonde hair or they shaved, but it's never a bad thing. I'll be honest, I shave my arms and I'm somewhat athletic too. I have for for a few years since my cheerleading days. I just think it looks and feels better, but there's nothing wrong with keeping it natural either.
I would not say 'cool' because most people don't think it is normal. However, I happen to think you have the right to do whatever you want with your own body hair. If it makes you feel better to be hair free and your girlfriend likes it, lucky you! Go for it! I am also a normal guy and don't think there is anything wrong with clean shaved bodies. If models, swimmers, bodybuilders, basketball players, cyclists and people with tattoos can do it, why can't anybody? It does not affect who you are. I wish people would be more relaxed about guys shaving.
I don't really know how to answer the question of whether or not, "it's cool", but it's important to do what you want. I'm sure there are a lot of people who think, "ew" when they see or hear about a guy who shaves his body like that, but honestly, I don't think that many people care. Most just pretend to, in my opinion.