I've only made a few splices and used a band saw. A miter saw or dovetail saw will work if deep enough. Any saw you can control should work. Just take your time and go slow.
If your splice cutting doesn't come out too good you can boil or steam the two splice parts, put them together and clamp. After a day or so you can take the clamps off and you will have a better fitting splice ready for glue up.
Another note: shape your handle close to the ultimate size before cutting the splice. If you don't you will remove most of the splice by cutting the handle to shape.