After reading about someone's difficulty slitting tennis balls for use on a walker, it occurred to me that a holder could greatly simplify the process, and perhaps help avoid injury. This is the first shot at a 3D printable holder. It's meant to be used with rubber bands to help keep things together while the ball is slit with a box cutter or razor knife. While investigating commercial alternatives (>$100, by the way), I found that teachers also use slit tennis balls on the feet of student desks to cut down on classroom noise. Perhaps you have another use.
This is not a stellar OpenSCAD file, but if you can decipher it the variables below should help you modify things to your heart's content.