Phil, what I always did whenever I bought an old rifle was to dismount the stock(s), [in your case then sand off the mold/mildew], then strip off the old varnish/lacquer/whatever and sand, sand, sand. To strip use a good quality wood stripper, and what works well is a straight razor blade - just make sure you get it all off. After you're satisfied with the final finish (using successively lighter grades of sandpaper), it's time to pour on the linseed oil and rub it in by hand. You'll want to do a number of applications, rubbing it until you can feel the heat - this way the oil will soak well into the wood. You'll be amazed at the final finish! Do enough of it and it will keep out the nasties as well.
I've done quite a number of old rifles this way and it works... gives the old girls some dignity!
BTW, I'd also invest in a dessicant for your gun cabinet - you obviously have moisture in there.