The one on the left is for fittings where the spanner holes are at surface level. It was made from 1/4" key stock from a hardware store with a chain master link for connection on the end. It and others have drill rod pins hardened and ground to size.The large diameter one with the delrin end is for bezel rings to hold the ring in place and start it in the threads without touching the lens. The others are for use where things are recessed. The one with the delrin pilot goes through a 5/8" hole, holds a round nut to thread on axle, then retracts as the nut is tightened. I made them for frequent use specifically for optical work.
Not knowing what your light is like, I think one similar to the one in the right front with the hole would allow the spring to go up inside and still get a grip on the reflector. It may be possible to just use pins a bit longer so the tool body stays above the spring and the pins are bottomed out in the holes. A hardwood body and nails may work just fine for your application.