Sanding the factory grips is an interesting idea.
And if it's good enough for schmeky it's good enough for near anyone.
I'm a bit of a woodworker and recommend that you start with 60 grit and sand evenly until the checkering nearly disappears.
Then use 100 grit to remove the last traces of checkering and any scratches left by the coarse 60 grit.
Once all signs of checkering are gone, smooth them up with 150 grit paper.
At this point, I'd recommend you purchase a can of Watco Danish Oil (or any other wiping oil) in the color of your choice. Natural would be my choice. Coat the panel liberally with the oil and, while wet, sand with 220 grit wet/dry sand paper to make a fine sawdust that will mix with the oil and fill the pores of the wood. Wipe the oil off delicately so as not to pull the slurry you created out of the pores.
Let the finish dry. This may take a couple of days.
Repeat the wet sanding process if the pores in the wood are still readily visible.
Once the panels are smooth enough to suit you, just apply light coats of the oil finish. I suggest you apply at least 3 coats total.
I think you just talked me into doing this very thing to my unused pair of walnut grip panels.