If you don't do as Howdy says (replace from the left), you can replace the cylinder from the right, but you have to rotate the cylinder clockwise to cause the edges on the back of the cylinder to push the hand back into the frame, and some guns won't do it, depending on the hand spring strength and the edges, so the hand needs help, using a stick or small tool or your finger to push it back out of the way.
The conversion cylinder by Kirst is designed to replace from the right, as there is a hand channel in the backplate.
The R&D conversion cylinder can go either side, by rotating in on the right, or rolling it from the left as Howdy Doody says.
By the way, Howdy, Howdy Doody, I don't miss California much, but I do miss the Western 3gun matches, there are none here around Tucson, but plenty of CAS/SASS matches.....Flint