You can have conscious sedation anesthesia. In my family the combination used has been Versed, Propofol and Fentanyl. Muscle relaxants are fine, but muscle paralyzing agents are not (succinylcholine is the one that can trigger MH symptoms). Your anesthesiologist can help you figure out the best anesthesia for the lithotripsy.
For local anesthesia the best choice is Carbocaine or Marcaine without vasoconstrictors. However getting a local shot with epinephrine will not hurt you, but it will likely make myotonia worse for a few hours or days.