If I were you, I would at least try to borrow a 12 gauge, and use nothing less than a 3 inch with 00 or 0 shot.
Buckshot is a great killer, but not if you don't thoroughly and completely drill that thing. A piece of buckshot is pretty equivalent to a high powered .22, and only a couple hits in less than lethal areas won't even slow a deer down.
Biggest shot possible, fastest velocity, and tightest pattern. with a tight 2 feet wide pattern, you will either very likely get several pellets on target, or miss completely. A five foot wide group very rarely will get a killing hit.
There's nothing wrong with using buckshot on deer, but there are some responsibilities that come with it.