I always remove the teeth. (step 5)
I use heat shrink as a handle to make it easier to grip (softer on my little paws

) and to keep my fingers off the metal. It is cheap and easy to do.
I have noticed small spots of rust where my sweaty fingers have been resting on the shiny section of the pick.
The next picks I create will be coated with clear lacquer before adding the heat shrink.
Hopefully this will protect the metal from my sweaty hands. The section which goes into the lock will get the coating scratched off, so I will have to spray it with WD40 every now and then.
I guess the pick will break or wear out before rust becomes a real problem.
You could even give the pick a coating of rust killer before lacquering.