If the chamber's tight you can use a fired rimfire case to test your firing pin. My when I had a free-pistol I kept a used case with a bit of cleaning patch stuffed in it, and would drop the firing pin on the used case (not always on the unused part of the rim) for the purpose of easing the springs.
In reality there's SO little priming compound in a .22 case that it's not at all loud or dangerous to pull the bullet (hand on the case, pliers on the bullet) and (if you're worried cover your eyes and ears, and wear gloves) point the case opening away from you and scratch around inside with nail or straightened out paper clip until the tiny little bit of primer discharges. If you think that's too risky, pull the bullet, fill the case with water or oil and wait a week or so, and then scrub the priming compound out.
But - seriously - the primer in a .22 case is nearly nothing.