Cut a piece of hickory dowel rod that is 16 to 18 inches long. Different lengths of mallet will suit different musicians, so feel free to experiment to find the right length for your needs. Sand the shaft and coat with polyurethane stain. Allow the stain to dry completely so that you have a hard coating on the shaft.
Insert a wood screw and washer on one end of the shaft, and tighten down so that the washer is tight against the end of the shaft. The washer should be larger in diameter than the shaft--an overlap of about 1/8 to 1/4 inch is suitable.
Place your lacrosse ball into a vise and drill a hole all the way through that is 1.5 inches in diameter. Clean out the hold of any residue, and spray a small bit of WD-40 or other lubricant into the hole--this helps in the next step.
Coat the shaft of the mallet with glue in the area directly behind the washer, extending back about 1 inch. Now slide the lacrosse ball onto the shaft until it reaches the washer. Allow the glue ample time to set before using the mallet.