I have a cork grip that I am going to sand down to fit the butt cap. Does anyone know the correct grade of sandpaper to finish the Job? i.e. 120,140, 400?

You'll want to use a lower numbered grit to do the bulk of the material removal. As you get close to the final size, begin working through successively finer and finer grits so you'll end up with a smooth surface. If you jump from a coarse grit to a fine grit, you won't like the result.

80 to 100 or so are great for rapid material removal. 150 is good to finish that part of the job up with. Then 220 and then 320 for smoothing the surface. Finish up with 400 if you want it super smooth.
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Not to important for anything under the cap, just make sure you have a nice clean square edge. Finishing the rest to 400 is fine, 220 is probably the minimum..

We start with a small flat mill-bastard file (about 3" long) with a medium grit to get the initial shape. Otherwise, use 60-grit paper, and then work up to 320-grit. You don't need fisihing-grade papers because the tenon that you are shaping will go inside the butt cap.

On the other hand, if you mean that you're shaping the grip to taper into the cap, I'd just keep progressing through 400 to maybe 600. We use 800, 1000, and 1500-grits (wet/dry papers) plus 0000 steel wool to finish ours, but I'll admit that's probably actually excessive.

Uncle Russ
Calico Creek Rods