Fimo is a very convenient material to make handles from. In case you don't know what fimo is: It is a plastic modelling clay that is malleable until it is cured in an oven. You don't have to cut slots or exact holes to connect the metal frame with the handle, and any desired shape can be obtained by kneading the Fimo, without grinding or using any tool at all.
This is the metal frame you start with. This one is welded, but it can also be bent from a single piece of metal. Whatever it looks like, it must have a stop at the bottom so the Fimo handle can never slide off.
Take the Fimo clay..
...and cover the handle part of the metal frame with it.
Now, squeeze your hand firmly around it. The impression of your fingers will give you a handle that fits perfectly into your hand.
There it is! You usually have to adjust one or two parts, wipe Fimo crumbs away etc.
Done! Cure it in an oven and you are ready.
Mixing two Fimo parts with different colors can result in a beautiful marble-style color mix. You can cut a checkering into the handle before curing. Fimo is strong enough to be used as a handle, but I would not recommend it for a whole slingshot unless you make it very large or use a metal skeleton that takes the stress.