I agree that there should probably be a way of excluding certain mobs when using cocoons. Too many times have I laid out an array of them only to return to feathers, raw chicken and a not-at-all suspicious wolf.
I was wondering whether breeding foods could play a role in animal selection? Feeding 5 wheat to the cocoon would restrict the pool to sheep or cows, for example. Using a gaia spirit and then a certain amount of a specific breeding food would instead bias or outright restrict the cocoon to the respective rare animal(s). It helps that most animals have at least one or two foods required for breeding that don't overlap with one another. I guess part of this stems from how obtaining villagers and shulkers with Botania bypasses the gaia spirit = rare spawn mechanic.
I'd also prefer moving rabbits to the rare animal category (if anything it feels like I see horses much more often).
More generally, I feel like the cocoon recipe could be made more similar to the GoG one except with mana string instead of regular string. Using pixie dust for what is most likely a dud doesn't feel great. What I can imagine is with the cheaper recipe, you could probably drop the default rare spawn chance to 5%, but using some pixie dust on the cocoon increases the chance to 25% or something. It would still bias rare spawns native to the biome, unless a gaia spirit was used instead in which case it's truly random. Not sure if or how this might interact with the above idea of using breeding foods but ah well, just some food for thought.