Umbilicoplasty has been one of my most requested procedures. Men and women both commonly request improvemetn of the belly button (outie to innie, smaller, etc.). If the problem is restricted to just your belly button, then yes, you can have an umbiliocplasty without a tummy tuck. However, if it if more tof the loose skin around the belly button, then a tummy tuck may be better - which will also include umbilical revision. Some of my patients have the loose skin aroung the belly button but do not want a tummy tuck. In these cases, they have gotten improvement with an umbilicoplasty followed by a series of laser skin tightenting for the skin of the abdomen. You obviously need to be fully evaluated by a plastic surgeon and I am happy to take a look at you.
It depends what you are trying to achieve and what the issue is, but in short yes it is possible. I would recommend you see a board certified plastic surgeon to go over your concerns. Good luck.