thats a good question, and though im not certain i THINK that most of the mushrooms that grow on materials so composted, they require that the material has quite a lot of fibre, and from my understanding (ive never touched worm castings other than those in the bucket with my canadian nightcrawlers ive purchased for fishing purposes) WC does not have
enough fiber
all that being said you can grab spores sometimes from the mushrooms at the store whose veil has yet to break, ones with exposed gills will most likely have dropped all their spores already, to do this you remove the veil with a sterile knife and put them on a piece of printer paper or glass underneath a jar or bowl for 12 to 24 hours and make your own spore syringe with it
but i dont think that white buttons will be the right kind to try with it
i would try oysters because theyre very adaptable, and possibly a poo eater of some kind, there are many poo eaters out there, but the only ones i can ever seem to remember (because i only cultivate oysters so far) are the psilocybes, which you would likely be legally restricted from harvesting a crop from, but a similar, more legal poo eater might be a good idea for you