Taxidermy Skill that must be leveled up. Possibly install a quest of multiple parts so it is challenging which in return makes it rewarding to accomplish. Would use elixirs, solvents, cures, etc and have its own tool set.

Either use any mob you kill by removing the skin with the proper tool and then stuff it with the proper resources, tools and skill level or just make it for tamable pets. End result should be a lifeless full size replica of the original mob/pet with stat menu removed. Upon mouse over it could simply note what the creature is and when it was stuffed with makers mark if the taxidermist so desired.

Taxidermy skill would allow all stuffed creatures to be full size to display as deco in your house. Pet leash only allows a few shrunken pets to be anywhere near close to real size.