Except for being more careful, are there any tips or tricks for preventing the final splitting when using a handsaw?
The simplest is simply to put some masking tape on the exit area. This will (more or less) hold the wood fibers in place and prevent the saw teeth from splitting them off the body of the wood.
However, this will work best for tough woods and sharp, fast saws, since the less stress you put on the fibers the better, and the smaller the cut per tooth the better.
So, depending on your tools and wood, you may need to clamp a piece of scrap backing wood to the exit area. Then the cut at the real piece will be smooth, but you may have tearout on the sacrificial piece - which doesn't matter.
EDIT. There is a third way, but I don't recommend it.
Start a normal cut, and go nearly all the way.
Stop, reverse the wood, and use the kerf to guide the saw in the opposite direction. Continue the cut until partway through the exposed edge.
Now flip the board and make another cut like the second but finish the cut.
In theory, all cuts are made with the surface fibers being pushed into the surface of the wood, and tearout will not occur.
However, there will be opportunities for the edges of the cuts to not line up exactly, leaving an end which is not a smooth surface and which shows the three cuts. This might not be a problem for ends which will not be exposed, but the whole technique is fiddly and I don't recommend it.