[dfariswheel]

Here's what I've done a few times.

Soak the grips in lacquer thinner or a good quality wood stripper like Formby's to remove all the old finish and clean the wood.
This will not harm the medallions, so leave them in place to prevent cracking the grip attempting removal.
Use a solvent-proof toothbrush to lightly scrub the checkering.
After thorough drying, LIGHTLY sand the wood where needed.

If you have the tools and skill, you can point up the checkering with a set of checkering tools.

Colt used a stain-finish to finish grips in those days. This was some sort of varnish with a reddish stain.
The closest I found to factory was Minwax Satin PolyShades Old Maple.
This is a polyurethane satin finish with a reddish stain. The satin is a closer match to factory then the gloss finish.

I recommend brushing on two to three coats, lightly sanding between coats after each coat is thoroughly dry.
For a smoother finish I'd spray the last coat on with an airbrush to leave a final finish without brush strokes.
Factory finishes didn't totally fill the grain but if desired you can add coats and sand more between coats for a smoother look.

I thin the Minwax with about 5% paint thinner so it'd brush easier and with less brush marks.
I'd thin the airbrush coat more to allow a good spray.

The final look is very close to the color of the original Colt finish.

 

[dfariswheel]

I also have long used leather dyes as wood stains.
One that works very well is Tandy water-based dyes.
These come in many colors and can be easily blended and thinned to lighter tints with alcohol.

You can get most any color you want by mixing, and the dye soaks into even oily wood very well.
For darker colors the solvent based Fiebeing's is great, but you do need to thin it with the special thinner or you can dye the wood too dark.

However, for an authentic Colt grip finish the Mixwax PolyShades is better because that's how Colt did it.