I'd check the owner's manual or Remington's site for information and lube it (or not) according to their instructions. If they don't specify exactly, I don't see any real problem with your method.
Still happily answering to the call-sign Peetza.
You do not HAVE a soul. You ARE a soul. You HAVE a body.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.