You don't specify the smallest size you want to use. I have bits so small that I don't dare drop them because I may never find them.
I have two drill presses, a large floor-standing, and a benchtop model. Both have the WEN DPA167H chuck mounted on them. They advertise 1/64-inch as the smallest size, but I have used smaller bits. I kept the original chucks in for larger bits or drilling steel. So, yes, you can change chucks with the proper tools. Note that there are a few cheaper drill presses that do not use taper-mounted chucks.
I have a Dremel mounted on a drill press stand for bits too small for the Wen chucks.