On most Uno gearboxes (probably all except Uno Turbo), the inner driveshaft joint is the 'tripode' type, running inside the differential. It is held to the driveshaft by a simple circlip that you can see and remove with circlip pliers. This is after you remove the driveshaft from the differential - drain the gearbox oil first, otherwise it will come out when you remove the rubber boot.
I would leave the outer CV joint in the hub, unless the boot has been split for some time. If it has allowed most grease out and dirt in, you'll need to take apart and completely clean the CV joint, wiping away all grease with paper towels.
There is a different type of circlip (without holes for pliers) that holds the outer CV onto the driveshaft. This one is difficult to see, being buried in black grease. Sometimes there is no circlip and instead there is a 'jump ring' on the end of the shaft which locks inside the CV joint - you can't see it. This type of CV joint can be removed by knocking it off the shaft with a heavy hammer - difficult to do, particularly if the CV is still in the hub bearing.
Therefore, it is best to leave the outer CV attached to the driveshaft as the others have said - remove the inner tripode joint instead, to slide the outer CV boot over the shaft.
Some Uno inner joints (1372cc) have a boot with a bearing. Don't try to remove the bearing from the shaft - it is easy to damage it and difficult to get the bearing in the right place for re-installing. Instead, stretch the new rubber boot over the bearing.
Please also see the thread
https://www.fiatforum.com/uno/22091-uno-60s-driveshaft-seals.html
-Alex