Probably a dead thread and all but my dad explained that the best way to drill through veneered wood or soft 'splintery' wood is to cover the section you are drilling with thick fabric tape such as elephant tape, it is best to do this prior to putting the final lacquer coat on because you might have to remove excess adhesive left over from the tape depending upon its type (for this I recommend using solvent based PVC Cleaner, better than white spirit; but be careful because some of this stuff leaked on the floor outside and managed to make part of the tarmac drive soft again) . Also if the drill bit has what appears to be rotary saw blades arranged in a circle to cut the hole out, drill it so that these little triangles point downwards so any veneer etc are puched into the wood rather than being pulled up.
It might be too late to help OP but if this post has helped anyone else then
Lewis