There are many types of musks, which all smell different. So if a deodorant has musks in the base, do not assume you're not going to like it, it could be a different musk that you actually like. I have not smelled the old spice you cite, so unfortunately I don't know what it smells like exactly.
My favorite scent for a deodorant is Caron pour un homme, lavender and vanilla, very classic. I don't perceive it as musky, but of course, there's no way to know unless you try it.
Btw: I did not know about tea tree oil. It seems to be quite popular with beauty products for either sex- hard to think it has such effects. But who knows ...