Cutting splices by hand:
It all comes down to accurate marking out, and good quality tools.
The sides and belly should be planed flat and squar,. Not easy if you don't have the tools or experience.
Mark the splice on the back . The flat and square surfaces allow you use a combination square to project accurate lines around the sides, to the belly. Mark up the lines belly and you will have identical sets of lines on both back and belly.
Mark out waste area on both sides of both billets and double check that the correct areas will be cut.
Cut from both sides rather than sawing from one side and hoping the cut will stay square. A spliced handle is going to be 1.5 to 2" deep, from back to belly which is too much for most people to cut accurately with a handsaw.
When you cut from each side you first saw to the other side only at the top, then down the handle staying on the same side, the blade doesn't go through to the other side . Then flip it around and repeat. This leaves a hidden peak of material in the middle which you then cut. The billet now has kerfed partial depth cuts on both sides so sawing down the peak is easy as the kerfs guide the sawblade from one side to the other of the billet.
You need a good saw, either a very large western tenon saw rip cut teeth with a back on it to stiffen the blade. You will need one the allows at least 4.25" depth of cut. (expensive for a new one)
Better off getting a Japanese pull saw, with rip cut teeth, as they don't need a blade stiffener, so they can cut 4"depth no problem.
If you don't have any experience practice on some scraps, both squaring up and cutting.
Hamish.