Grip shifters are cheap ($15 or less at a LBS- they might even give you old busted ones for free if they have them sitting around for some reason), and should be easy enough to remove the indexing on with a rasp, sandpaper, grinding wheel, etc., as they're generally made entirely of plastic. I have no idea what the pull on the cable is, but make sure your brake springs have a strong pull, so that everything returns to position.
Since this is on a 'cruiser-bike-for-looks', I think the biggest problem might be the amount of rotation in your wrist to actuate the brake. Hopefully you don't actually need to use the full range of the shifter's motion to pull the amount of cable you need for your brake.
Edit: If you're really going for looks, I suggest just going with a coaster brake. grip shifters are the epitome of cheap plastic junk, and cables are rarely attractive
