If the leather has a finish wax/polish on it you'll just be putting a leather conditioner on top of the wax/polish; probably a messy combination.
This might not be the best way to handle it, but it will be fast: remove the wax/polish with 300-grit (or thereabouts) sandpaper. Protect the adjacent butt wood with a couple turns of masking tape, then lightly stroke the sandpaper over the leather. Rotate the sandpaper frequently and use a terrycloth towel to clear loose wax/polish from the leather. It really helps to use a magnifying glass so you can see the difference between waxed leather and clean leather. Once you know what the difference looks like you can do it without the magnifying glass. You probably won't be able to remove all the wax without removing too much leather also. 70-80% removal should be enough.
There are liquid wax/polish removers but they're for use on solid surfaces like linoleum, hardwood floors, etc. I'd be nervous about what they'd do to leather. Maybe do a search for leather wax/polish removers.