Engine balance after new pistons
The H116CP's are SUPPOSED to be stock weight replacement pistons. So really you can 'probably get by with it' if you want to. But, there is more to just balancing the new and old piston + pin + lock weights. To do it properly, you also take all of the rods into the shop and they weight the large and small end weights on each, and then grind on the heaviest ends make them all equal. Once that is done, then the bobweight can be computed and then any crank weight adjustments can be done. They won't need the old pistons. They will need rings, pin locks, and bearings (at least one set of these) and the flexplate and damper.
Now, if you buy new SCAT rods for example, then they come weight matched end to end and the shop does not have to do the rod work. Since the rod end to end balancing is usually the most time consuming part of the work, you should be able to pay for a substantial part the new rods with the balance work savings.
With the heads you have, you're gonna be able to turn some good RPM's so balance should be done IMHO if there is any question.