First off - can you legally use a handgun during your bow season? Second - if you are looking to fill your freezer and not wanting a deer to slip by you out of bow range either leave your bow at home and use the handgun or become a better bow hunter by increasing your effective range through practice or tune up your stalking skills.
When I archery hunt I only carry my bow. I can expect animals to be seen out of range. Heck when I hunt with the rifle I see my quarry out of range sometimes. I think you see where I am going with this.