I'm low tech and a bit laborious but it gets the job done for me. I'm not making hundreds of them though, so dismiss if you are into production efficiency. Sharp utility knife, ruler, cutting board. Cut a strip from the veneer sheet. Put black ink dots along one edge all the way down (face and endgrain). Cut strip into squares.
Take to lathe. Face maple dowel with bored hole already to final size. Double sided thin tape (two strips is enough) applied to dowel face. Smack veneer square onto maple face. Slowly bore veneer ID with live tooling (endmill)....just plunge at final depth. Leave OD of veneer alone. You can touch up the edge with some paper after boring if you want to remove some fuzzies right then. Carefully separate from the double sided tape with a utility blade WITH the grain to prevent splitting. It only takes breaking one or two to get the hang of how to orient the veneer against the two strips of tape and where to slip the utility blade in to spearate it from the tape. Often, the tape will stay on the dowel and you can cut several veneers with one taping. Any glue residue left on the veneer, SCRAPE with utility blade right then.
The veneers being in square form make it easier to slide on tenons and line them all up and in the same direction according to the black dots so that they change brightness in unison as you rotate the finished cue. Trim square corners off with bandsaw after curing.
I do whole sheets basically the same way.
