Well Jim, I've had good results with that. Just recently did it to a Parker Repro A1 Special--I think essentially the same issue: had not been fired in about 20 years. Grease etc can "set up" in that time, and I'm not sure what harm it would do, since it dries very quickly and is not another lubricant itself but rather a degreaser. I certainly would not recommend using oil, because in a situation like the poster described, old lubricant is likely the problem rather than the solution--and, as you indicated, you don't want to let it seep into the head of the stock.

The Repro doubled on me 2 or 3 times before I treated it. Afterwards, several flats of shells fired, perfect function.