another no4 mki* refurb project

[Sunray]

"...Big F'n screwdriver!..." That'd be a regular 12" screwdriver.
"... dried cosmoline..." Dried or not, Cosmoline is just thick petroleum jelly. Best dealt with using mineral spirits.
"...It now jiggles..." Most likely caused by the wood shrinking over time. Don't do anything until after you've cleaned the stock and see if Nature
re-moisturizes the wood. Just the cleaning will help that. Then, if it does not swell a bit, use either regular brass shims or a bit of leather. The thickness of said leather will vary with how much wiggle is left.
The hand guards will vary in colour and type of wood. Not all of 'em are walnut.
"...scrubbing the stock..." Soak 'em in mineral spirits too. Then wipe off the sludge(that does not get dumped in any drain), then use the Murphy's.