OK, Uno five-speeds come in four distinct types:
1. - '84-'88 Uno 70, has shift lever with two rods, one operates crank near bottom of gearbox and other operates vertical rod with link across to selector on top of gearbox. Easily recognisable by passivated-cadmium plated ("gold" coloured) tin cover on top of gearbox. This is the same type of gearbox as fitted to FIAT 127. Has the tripode-type driveshaft joints in diff.
2. - '88-on Uno 70 (may also be earlier), has shift lever with two rods but one is fastened directly to gearbox selector, the other pushes a small link rod to twist the selector. *This is the 128-style gearbox and should be the same inside as your X1/9*. This also has the tripode-type driveshafts so the diff should be the same as your X1/9 also.
3. - '85-'88 Uno Turbo "bottom linkage gearbox". This is based on that in the Strada. I have heard of people using the gears out of this to improve a 128 box, so I think it must be the same as the gearbox described above. This has inner CV joints.
4. - '88-on Uno Turbo "top linkage gearbox". Not to be confused with 1., it is totally different because this gearbox is the Tipo design. The selector is mounted on top and the gearlever linkage runs inside the car. This also has inner CV joints.
As you may have picked up, 1. and 4. are no good to you at all, while 2. and 3. are basically the same as an X1/9 box except that the single selector comes out the wrong side. This should not be a major problem - you will just have to use X1/9 casings etc. while the gearsets should be interchangeable.
Sorry this post is not terribly specific, but it is intended to help you avoid the two Uno 5-speeds that will be no use at all, while (hopefully) encouraging you to take a look at the other two!

Look for Uno 70's from around 1988 with the single selector at the bottom of the gearbox. Or, earlier Uno Turbos but the driveshafts will be more work and of course the gearbox might be more stuffed!
-Alex