The geometry did cost some effort, but after several tries I had a handle that can be used by regular sized male and female hands. Here is one tip, I'd like to share: in order to save material I printed out several paper templates. It let me determine the workability of a given design without cutting and I had the chance to use up scrap pieces because I could verify the design will fit on a certain part.
I used 20 mm plywood which is coated white and cut it with my Stepcraft desktop cnc-machine and a special 3 mm endmill for wood. As the cuts are quite deep it's a good idea to attend the cnc and use the vacuum from time to time to clear out the path.
After cutting I sanded all parts and rounded the edges. Eight 20 mm hex bolts are screwed directly into the handle. Washers and some grease make for smooth and quiet rotation. The wheels actually don't need to spin free. A bit of resistance does not hurt.