Use a good stripper like Formby's to remove the old finish.
Use a solvent-proof toothbrush or other small brush to scrub the finish out of the checkering.
Let the stripper do the work.
After stripping, do as little sanding as possible, staying away from checkering and grip medallions.
Make sure to keep the bottom of the grips flat, and be careful around edges so you don't remove wood and alter the tight match between the grip halves.
Apply whatever finish you want.
Colt used a stain-finish for their grips. This was a reddish stain mixed with a varnish-like finish.
The closest I found to Colt the factory finish was Minwax Polyshades Old Maple.
This is a reddish stain mixed with polyurethane.
The satin finish comes closest to the factory look.
Usually, three coats gave a good finish.
You can buy Polyshades in most Walmart's and hardware stores in small cans.