Depends of the handmade strap.
If it was built to fit tang then it will be not possible to put a deployant on it.
The one in picture looks to be a 24/24 mm so IMO it will not fit your dep clasp as it is 22mm.
Now, a strap maker such as Gunny might make it thinner at the place where to attach the deployant. But the exact choice of leather may be limited to allow for so thin a strap. Worth asking somebody. Who knows?