Wolf,
Assuming that the end you want to stop splitting is about 22mm.....
Get a short length of 22mm copper plumbing pipe, and a socket (from a socket set) that the small end will just fit inside the pipe.
Lightly tap the pipe over the socket until it expands into a flared out shape.
Whittle the end of your stick until the end is a very tight fit,
then tap the stick into the pipe on a hard surface - once it is on sufficiently, you can trim off the excess pipe and file it smooth
Even 15mm pipe will stretch out a considerable amount if your stick end is smaller.
Or a good whipped finish using stainless steel wire.
ATB
Ogri the trog