Interesting question, but not enough information. Is it a solid wood or plywood uke? What type of finish? Was there an endpin, i.e. is there a smaller hole there already? Is there an inlayed piece across the end seam? All of these things make a difference in how you could do this. Safest is to drill it smaller and then expand the hole with a reamer. Reamers are expensive. I've done it on a lot of guitars with this method. Obtain a very sharp 15/32 bit. Drill a smaller hole through the end, say 3/16. (guitars usually already have a hole for an end pin or for a screw to hold one) Cover the hole with a piece of strong tape. I don't like the speed of an electric drill to do this since whats done is irreversible. Make a handle for your bit, I use a vice grip pliers. Using your small hole as a guide, slowly turn your bit to expand the hole out to 15/32. If you push too hard the bit will grab and you are screwed. Once you have expanded the hole to the full width of the bit and drilled in a little you can chuck it in a drill and safely finish the job. I could give you some more tips if I knew more about the actual uke you are drilling. I have done this on about 100 guitars through the years with no problems. Had I known it would be so many I would have bought the reamer years ago.