Haven't done it myself, but I'd say the most important thing is to not short anything out. A lot of 1u cases already come with a plastic sheet on the bottom.
Maybe see if you can get some sort of stand you could tape or screw into the case and then the NUC onto that. Maybe NUC board to itx screw holes adapters exist, don't know.
That's where I'd start, next thing is getting the ports accessible. Most stuff is available as keystones, at least USB and such. If you can 3D print, an adapter for the io shield to hold some keystones shouldn't be too hard to make.
Add some case fans as well and that's about it I'd say.