IIRC, the HP 22 is hammer fired, with a strut and spring that fit down in the rear of the grip. If the misfires are due to a weak spring, it is the hammer spring (aka mainspring) that would be the problem, not the firing pin spring, which holds the firing pin back rather than propelling it forward.
There should be a screw holding that end plate on; remove it and the plate slides down, again IIRC. Watch out, as the firing pin and spring can pop out and get lost.
Gun Parts Corp. (
www.gunpartscorp.com) has parts for that gun.
Jim