As you can see, other than for a smallish flat on the bottom it is curved every which way. How would you fixture it for milling and aligning the second side - mill out a negative pocket and fix it temporarily with double sided tape or blue tape/CA glue “trick”?
(I know this won’t be nearly as charming as a hand carved version).
If you have the model to cut it, you have the model to cut a fixture.
My inclination would be to machine all the way through the stock used for the fixture and secure w/ blue painter’s tape and cyanoacrylate glue only at the bottom, then do the belt-and-suspenders thing and have an initial operation which mills some flat areas down to a bit more than the roughing clearance, secure those with clamps, then machine the balance, then remove the clamps for the finishing pass(es).
Ooh, I really like that. No fixturing, and it solves the potential problem of downforce on the cantilevered handles flexing things causing small (or large!) movements.