The easy answer: if you're worried about hitting the side, use an airdodge, then bike. If you're more worried about the ceiling, use a fastfalled Fair (hold down on the control stick while you C-stick the Fair), then bike.
If you don't have your Bike, instead use a Jump towards the stage. During knockback this will send you super high, so you may have to DI so that you're sent lower than the corner (where you'd usually want to go), so that you don't die from the jump going too high. It.... sorta depends on the amount of knockback, and your proximity to the side or ceiling killzones.
If Fair and Dair are really the same # of frames long, then you can use either one; but you have to do it differently. Do not hold the control stick down + C-stick the Dair; that ruins the fastfall. Either use the control-stick + A button, or C-stick the Dair. In either case, Dairs can be finnicky, so tap Down afterwards just in case. Or just use Fair, and hold down while you C-stick forward.
There are more complications though. At low percents (or rather, shorter-distance KOs), you're better off using a fastfalled Fair (or Dair) instead of the airdodge. For longer-range trajectories, the airdodge becomes better; unless you're headed vertically enough that you need the fastfall from the aerial. We're not sure exactly where the tradeoff occurs.
Also, if you're holding an item, throw it instead of the airdodge or the Fair/Dair... then bike.
Rawr.