You do not need the adapter if you are using the matched set of those gears and the diff they were installed on. You do, however, need a pinion depth gauge, and a few other pieces to properly set up gears. A shop usually charges $150-200 to do it, which is about what the tools cost. Plus, you would need a pinion bearing that is honed out so that you can remove and replace it without a press, plus another pinion bearing that will be the final part that actually gets installed. You also want to change the axle bearings at this time as well as all the seals, so you would need a rebuild kit. If you are going to have it done professionally, I would bring them both axles and let them do the tear down so that you reduce the chance of contamination. I will also note that the S trucks used gov lok diffs that are not the best design for strength.