I would take the grips off first. Keep them away from the aerosol stuff. I know many of the chemicals in the gun scrubber stuff are the same as the brake cleaners and carb. cleaners. And, from experience, I know carb cleaner will melt some plastic grips (have an old Ruger Mk1 with smeared spots in the nice checkered grips).
Wear safety glasses or goggles - you do not want any to splash back in your eyes. Know that from experience, too. Still have no idea how I got to the shower from the garage that day I was cleaning a carb out for a rebuild.
You may still need something like an old tooth brush to do a little scrubbing after a spray or two of cleaner. It evaporates pretty quick, so be ready to scrub quick.
After it's clean enough to suit you, you need to get some oil/lube back on the metal surfaces or they will rust. Just let it dry first (take maybe 5 minutes, depending on how much puddled up in the cracks/crevices inside (a heat gun or hair dryer might speed that up some, just get it warm, not hot.) It is the only thing I use rem-oil for - spraying oil back into the cracks and crevices you can't reach with the oil bottle dropper.