Is it permissible to have an electrolysis done on Chol Hamoed?
If it is possible, you should arrange the electrolysis appointment for a different day, and not schedule it for chol hamoed.
There are two potential issues with doing electrolysis on Chol Hamoed, taking a haircut, and doing melacha that needs a professional. Regarding taking a haircut, since it is not on the persons head, it is permitted. Regarding doing melacha on chol hamoed, although it may be considered a bodily need, which is permitted on chol hamoed, it isn’t needed specifically for chol hamoed, therefore it should not be planned for chol hamoed.
O:CH 531-8, Chol Hamoed Khilchoso3-8, 7-36, Conversation with R’ Farkash shlit”a author of Chol Hamoed Khilchoso. Other poskim hold that it should not be done at all on chol hamoed.