I just took apart my Cynergy Shotgun to have an adjustable comb installed on the stock. While I have it apart, I noticed the insides were pretty dry...should I leave well enough alone or clean and oil while I have the chance?

a light coat of breakfree (a very light coat) is all you should need. when i had my O/U apart i sprayed the workings with break cleaner (like you get at the auto parts store) let it dry then a light coat of breakfree. don't forget to use grease on the hinge

Oil is hard on wooden stocks and too much oil will soften and ruin them. I use a light film of gun grease on the metal inside and out and apply a dab to the hinge on my double shotguns. Take care...
Oberndorf

All above make good points but I prefer a light coat of synthetic lub on moving parts. This stuff still lubs after it is dry so it doesn't get into wood, draw dirt or freeze up in cold weather.

I would take advantage of the opportunity.

I agree with the synthetic lube. I spray mine with Rem oil or Triflow and let it sit for about 10 minutes then blow out the action with air to remove excess. I do this with all my Brownings, Berettas and Parkers.