Making Small Boxes

So I was intending to use a board of white oak I recently got to edge the plywood on my miter saw station build but as I edge jointed and flattened the board I started to see some characteristics I didn't expect. The planner made this far more obvious. Unfortunately I wasn't really thinking at this point other than getting it to the needed thickness (3/4") from the 4/4 rough sawn thickness. So now I have a 3/4" thick white oak board that needs a better purpose and I got to actually thinking again. The idea to make my grandaughters some boxes came to mind as well as the thought I hadn't done this before. Cabinets, shelves, entertainment centers, and the sort no problem but never decorative boxes. So I realize 3/4" is a bit thick for such boxes, I think, and my 3/4" won't likely be able to be resawn on my bandsaw and yield 2 - 3/8" usable boards. But then again I have no idea what guideline to use to determine the necessary thickness for these square/rectangular boxes but was thinking probably 3/8" - 1/2" to be likely candidates.

I had wanted to use my dovetail jig (Porter Cable 4216) to do through dovetails but need a bit more practice and I'm unclear as to the minimum thickness I can use with that procedure. So if any of you kind folks can guide, point, shove, kick me in the right direction it would be wonderful. I think it may be time to try some delicate work for a change. Not quite ready to try bandsaw boxes although they do look interesting and my Laguna 14-12 should be more than capable it will have to wait till another time.