Biggest problem with the bandsaw is you'll have a lot more cleanup to do than after the table saw, which means it's much more difficult to get the lid to mate perfectly with the box.
Do exactly what Tom said, then clean up with a block plane. If you find the lid and box aren't mating well, double stick tape a sheet of 180 to your table saw and sand the entire box top and lid bottom until perfectly flat.
Then glue on 5/32" banding to both the top and bottom, use flush trim bit and/or sanding block to flush trim to sides, trim thickness of banding down to 1/8" at the table saw, repeat flattening process if needed.
A great step forward for your organization. Being able to just pick up a tool as opposed to look for it will increase your shop enjoyment 10-fold.
@Chestnut - I have four drill motors right at my fingertips. A small VS drill motor gets used fro so many things; drilling, driving, flap-sanders, wire brushes, grinding stones, buffing wheels