Jim,
I'd use Wonko's turkey baster method, then go from there for what you wish in the way of a final finish.
I would entertain the idea of using a coat of thin model grade superglue on the head [and even on the wrist] afterwards & before final finish is begun.
Hobby or model shops often stock three distinct grades or thicknesses or viscosities of super glues; thin, thick & gap filling. FWIW, kept in the refrigerator it lives a very long time. Sprinkled with common baking soda it sets almost instantly as the baking soda acts as a catalyst.
Do what you will w/that info, but best to run a 'test sample' first so you know what to expect.
I personally keep in mind that old wood does not much appreciate excessive recoil forces & that thot takes precedent over all others. Same thot is used toward older & softer metals, but w/pressures in mind rather than recoil. It's a happy combination for older guns that will, I think, help extend their lives.
I hope your project proves successful and to your liking. You might consider some before & after pics & share them w/us later.
Kind regards, tw