Among other things, I'm a saddlemaster trained in doing leather repairs and restoration. First, how old are the puppets? Are they cracked? If so, nothing will take away the cracks. If the puppets are old, natural vegetable dies were probably used. Tanning was probably done using animal urine as a fixant. The dies are not the problem, it's the tanning that has to be considered. 100% neatsfoot oil ( NOTHING cut with other compounds or wax) always has and always will be the best thing to use when there are so many unknowns. You can get the 100% stuff at saddlery supply, feed, and leather craft stores. Some outdoors stores might have it as well. DO NOT get anything that weather proofs leather. LIGHTLY and I mean L*I*G*H*T*L*Y rub the puppets with a lint free cloth that has been left to soak in a bit of oil for about 24 hours in a covered container. This allows for even oiling. Store your puppets where they can get even air flow. Neither too hot or too cold of a room works best. Keep them out, don't put them in a box somewhere in a closet. Leather likes to breathe. Do they have any mold on them or need a little cleaning first? If they do, rub them with a dilute mixture of white vingear and water and allow them to dry for a day or so before you oil them. They should only need to be oiled about twice a year or so. You might want to consider wearing plastic gloves when using them to keep skin oil and sweat from getting inside of them. These little beauties should out last all of us, if taken care of properly.

Hope this helps.