I don't know about the reaction between the lead and wood - i'm not a chemist, but it seems to have worked in pencils for over 100-years!

As for the cork, when i've installed my own recoil reducers - i usually pick up a walnut dowel rod of the appropriate diamater, insert it into the hole in the butstock and mark the angle at which it needs to be cut so that it's flush with the butt of the stock (under the recoil pad.)

Cut it at that marked angle, and then use a hand drill to drill a recessed hole at about 45 degrees through the dowell "plug."

Then a wood screw through the plug (with the appropriated sized pre-drilled hole) engages the wood of the stock, while the angle "tension" pulls the plug into the recoil reducer an secures it in place.

That may hold a little better than the cork.