
These kinds of cysts can be removed under local anaesthetic without even any need to shave, but most vets are use to the scalpel method.
the technique is to make an opening in the cyst, draw out the exudate and then pull out the lining of the cyst through the hole, trim it away and put in a stitch or use skin glue.
Try googling for 'Non surgical removal of sebaceous cysts'
I have given these details to several Friends within my breed whose vets have successfully used this method, it has avoided GA and in the case of show dogs loosing a whole season of shows due to shaving.
One of mine had this method used, but she was having a GA for something else.