The outside corner trim molding is just used to hide where two pieces of plywood meet at a corner. It has no structural value.
I would not hesitate to mark your location, as displayed in photo #2 with a pencil line, and carefully cut a "divot" into the trim piece that corresponds with the shape of your fitting, using a sharp knife, chisel, or exacto blade. I would then use some clear nail polish to seal the raw wood. I would then carefully drill a small bore shallow test hole in the location of the screw holes, and probe with a paperclip to check for void or structural member. Being as you are at a corner it should have a stud. If not, consider using "wall anchor" inserts to add strength. Mount your hardware with a skim coat of RTV behind it, and secure it to the wall.
Good Luck!
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Steve & Jan, Ava & Emma (Mini Schnauzers):
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