These rifles are collector's items with some value.
"Shining it up" will destroy whatever value it has.
The best course is to clean the metal with bore solvent or oil to remove any dirt or dried grease.
To do this, just gently wipe the metal with a cloth and oil or solvent.
As for the action being frozen.
CAREFULLY remove the wood, then liberally coat the metal inside and out with Kroil. Allow to soak for several days to a week.
This should free up the action so it will open.
Once it's freed up, carefully disassemble it, and clean out all the dried grease and grime.
Coat with a good lubricant like CLP Breakfree and reassemble.
If you don't know how to disassemble it, or don't feel competent to do so without damaging a collector's rifle, take it to a gunsmith.
The key here is NOT to damage the "patina" that has built up over the last 120 years or so.
Shine it up, and you'll cause a great loss of dollar value, and will forever destroy it's collector's value.