The lid was some really ordinary plywood that was covered with paper labels on both sides, and wasn't going to make the grade as a sound board. So that came off.
The interior of the box was lined with paper and that too had to go, as I needed to reinforce all the seams with some linings, and while I was at it I lined the box with a thin veneer of Spanish Cedar. A large neck block of Spanish Cedar to mount the next to as well. Now it smells like a cigar box.
The only scale I could get to work with such a small box was a soprano one and joining at the 16th fret in order to get the bridge in a reasonable spot.
The soundboard is one piece Western Red Cedar 2mm thick with 2 fan braces running from neck block to end of the box. They are very finely tapered with a peak over the saddle of 5mm and a bridge patch of cedar as well 2mm thick. No other bracing in the top at all.
Trying to come up with appropriate trim to get the look right was a bit of fun. None of the styling on my ukes suits this, so I decided to try for a bit of cigar box mojo. Found some label art on Google. Printed them out on good paper and applied them to the top and headstock. The bridge I tried to give a bit of a cigar vibe to it with the deep trench milled in for the tie block clearance. Trim in Gidgee to give that tobacco leaf color and texture. At least that's what I'm telly everyone.

Finished with several coats of Mirotone Satin lacquer.
Been strung up for a day. At first it sounded a bit choked and tight, but that is improving rapidly. And the volume and clarity is great all the way to the 16th fret. But I only know a couple of people that would ever play a soprano up there.
After building this one, I'd suggest that making your own box would be the way to go. Far easier to plan out your scale length, and your own wood work will be much better than most cigar boxes that you are ever going to find.