Depends.. when your done,what would change? I grew up in the oak cabinet craze and can hardly stand it. That being said, I have honey oak cabinets in my house. Refinishing isn't an option for me. Dyes and stain may hide it but it's still red oak under there and I know it.
Painting would be fine. I'll build some some day.
One tip would be to start with longer than you need. It is not uncommon for the tap to take an inch or two to square up and be cutting right. Wax is good for a lubricant. Just don't advance the cutter too much. Many light passes gives a far better result than trying to hog through it in two or three goes