I have similar concerns as you, John. I would like to have an O/A rig, but my shop is my attached 3-car garage. Personally, I would rather have the bottle on a sturdy cart or clamped/strapped to the wall. In the meantime, I just use MAPP gas for annealing.
As others have mentioned, the problem with Oxygen is oil in the line. The problem with Acetylene is flashback. Never open the fuel bottle more than 1/4-1/2 turn, so if you hear the hissing sound of flashback you can turn off the bottle quickly. . .hard to do if the main tank is outside.
The key is just to be careful with ALL pressurized cylinders. Shut them off when not in use, keep oil/hydrocarbons away from the fittings, and keep them secured so they cannot fall. Even an inert gas bottle, like Argon, can become a projectile if the valve gets knocked off. Remember, the valve fitting on the end of a cylinder is only swaged on, so treat it with care.