You don't have to worry about being a mechanic. Planes are fixed by enlisted and civilians. They are led by maintenance officers, though.
AFSCs that work most directly with aviation without flying include airfield management and aircraft maintenance. Some intel officers are assigned to flying squadrons and operations support squadrons. Aircrew positions other than pilots include combat systems officers and air battle managers.
Your only route now to being an officer is OTS. The AF usually has separate rated and non-rated boards (flying vs non flying), however, from what I can find online, it looks like for 2018, they are switching to separate civilian vs enlisted boards. Right now the AF has a pilot shortage and UAV operator shortage, and that is what they have been focusing OTS boards on. Out of 4-5 boards a year, only one of them was usually a non-rated board. You could be looking at a significant backlog to even get to a board. Also, you can put down choices for an AFSC, but you will get what the AF needs.