Hi Ingvar,
Nice work. You can try several coats of boiled linseed oil, or just a tad of garden variety wood staining.
I cleaned up my Mauser Parabellum grips a few weeks ago and used the linseed oil to get them back to colour again (boy, that stuff smells).
The grips were coated in a thick transparant varnish by the first owner. Several layers of paint remover and cleaning out the remains with a brass wire brush (long live the Swiss Rifle Cleaning Kits) left the grips stripped of varnish, but as white as the day they were made. Several applications of boiled linseed oil restored the colour. When the result is too light, it's just a matter of adding a new layer.
I applied it with a small brush, then rubbed it with a piece of cloth, but since you only have to work on a small area, I think you can skip the rubbing phase.
Before the the treatment:
And after:
