OK, OK, I understand completely]
Wow...talk about opening a can of worms. At least you have a good attitude, that will probably help you regardless of your sartorial choices.
More important than the coat is what's in it. Particularly the pockets. I'd recommend an Orthopaedia book, protein bar, black pen, and (if they let you near patients) an always-up-to-date patient list, trauma shears, some 4x4s, tegaderms, paper tape, and a switch blade so people know not to mess with you. Worked for me. Good luck.