A couple of thoughts.
If you have a "kink" in the chain (tight link), then it can cause the chain to skip, worst on the smaller cogs. Either crank slowly and watch the chain as it goes through the derailleur jockey wheels, or bend the chain with your fingers and crank, feeling for the kink.

A mal-adjusted derailleur will skip. Make sure the chain is coming off of the jockey wheel and up onto the sprocket perfectly centered. The jockey wheel will float a little bit, so it should also be centered.

Many "newer" derailleurs have a B-Screw adjustment to allow one to customize the derailleur body tension. Loosen the screw, and the body comes forward and the derailleur is closer to the sprockets. Tighten it for more clearance (important for the larger sprockets). I don't know if your "claw" derailleurs have this option. Hmmm, dug up an old Simplex Derailleur, and no B-Screw. But there are claw adapters for more modern derailleurs.