Been using WD-40 on grips for years. But might try a round, small, wooden dowel or skewer instread of a screwdriver so you don't scratch the bar, especially if you use a carbon bar!
I also use WD-40 to finish cleaning the front der.- I'll spray it off good with WD, let dry, then re-lube with a regular lube. Find that it does a good job of getting the gunk out of hard to reach areas. Just be sure to put a rag under the der so it doesn't run down to the btm.bracket.