The wood block is supposed to be used as a neck block....inside the uke. I'm assuming you're doing something other than a traditional uke with this?? Cigar box uke or something? You can get away with just a glued joint if the neck is fit very well. No gaps between the body and neck. I would usually use a bolt or glued in dowel for attaching the neck
A few years ago, someone built a PC into a beer crate:
So, how about taking a neck, a bridge and some strings, and seeing what is the most outlandish thing you can build a functioning Uke with. Video of it in action for proof.