Note that most UZI specific suppressor mounts are designed to work on an unmodified SMG length barrel which sticks out a few inches from the barrel nut and is just wasted space.  I’ve never liked them since they make the whole package too long.  Gemtech used to make mounts that were designed to be used with a cut down barrel that is only about 1/2″ beyond the barrel nut which was required as it would use part of the barrel as an additional contact point for alignment.
This results in the most compact suppressor setup for the UZI but:
1.  They don’t appear to be currently available anymore and would require someone to custom make one today.
2.  When you go back to shooting unsuppressed you need to figure out where you put that barrel nut.

The other popular option is the 3 lug mount which as you can see below is not as compact but you don’t have to worry about where you put that barrel nut.