Kevin,
I do not own a table saw either. I have a 9" el cheapo bandsaw ( ryobi ) that is it for power saws other than a saber saw and scroll saw. I cut the shape I want pick a side to be the reference for the squaring of the box and sand the box square. Really though Kevin these type of boxes look complicated but I have seen you do work that is MUCH more complicated than making this box really is. The ribbons are very easy to make. The bow has a couple of inside cuts and the rest are outside cuts and then just a matter of fitting it all together. I suspect the key to making one of these boxes is simply to take your time cutting out the ribbons. Keeping the ribbon thickness uniform is probably the most difficult part however with a little bit of practice it becomes easier to cut them uniform.
DW