A variable speed Dremel will work. I've owned several over the years, and I like the new lithium battery variable speed best. The power difference between it and the other battery-powered ones is substantial, and it is the only battery-powered Dremel that competes with the A.C. line powered ones at all.
If you are considering an A.C. powered Dremel, you might want to consider going to a Foredom tool instead. It won't turn as fast, but it is able, with the narrower tool handles, to fit into tighter places. I can't speak to the Dremel flexible shaft attachment, but it will likely have less lugging power than the Foredom, based on the different motor size and configuration, and the Foredom's option to use 1/4" collets is helpful.
I have used the Foredom with a large 1/4" shaft sanding drum to whittle out Garand lower handguards to get heavy barrel clearance. Since I had a drum the right radius, this job took all of 5 minutes to complete. Very convenient. A wider tool holder would not have let me follow the drum far enough up the wood to do it. If you go to whittling grips, whether you use a Dremel or a Foredom tool, I think you will find small sanding drums are a good way to go at wood with them. They are less prone to chatter or jump in wood than their toothed cutters. If you go to look at the Foredom at Woodcraft, you will see lots of carbide abrasive burrs for wood, including European brands, for this reason.
Nick