Hang in there Chris...

With a rust hole like that, that pipe was obviously causing trouble, so you haven't wasted any time so far! (Funny how I knew it would be more than just the O-ring that needed to be replaced

)
I believe it's easier to take both the driveshafts out of the gearbox if you're working by yourself. Leaving both driveshafts on the gearbox seems appealing but their angles will make removal of the gearbox difficult and refitting very clumsy, plus you risk damaging the diff casing if you force the driveshafts at the wrong angle.
Leaving the right-hand-shaft attached to the hub, and refitting the gearbox over it, seems like a good idea but is difficult in practice and needs two people. The driveshaft inner joints have to fit through a three-sector-shaped hole in the diff casing AND then engage in the differential. It's much easier to do this after the gearbox is refitted. Therefore, start by removing both driveshafts. This also drains the remainder of the gearbox oil.
There's no need to undo the bottom balljoints - you can swivel the hub far enough to remove the driveshaft if you undo the two strut bolts (easy) and the steering tie-rod end (fairly easy) plus remove the brake caliper (easy) and tie it onto the suspension strut so it doesn't fall off...
Don't forget to remove the tin plate from under the gearbox, next to the engine sump, which has a nut/stud near the inner driveshaft joint as well as the three bolts underneath (the gearchange linkage comes off easily at the same time).
Your Uno has a hydraulic clutch, so unbolt the whole bracket from the transmission - a few bolts - don't try to remove the slave cylinder from the bracket (probably rusted-in) and don't bother to undo the fluid hose as it may be difficult to bleed the system later (better not to interfere with something that's working...)
Take a critical look at the clutch itself, since you have to take it off to remove the flywheel. If the radial grooves in the friction lining are nearly gone, it'd be silly not to replace it. The release bearing commonly wears the spring fingers so it's usually best to replace all three, unless you're not expecting the car to live much longer.
Actually replacing the core plug/Welsch plug is very easy. It's shaped like a paint tin lid (has a flange around the edge) so make sure you get the genuine part rather than a standard core plug.
All in all, the job is not that difficult and a chance to fix any other wear items along the way - e.g. the clutch, the CV boots...
Let us know how you go,
-Alex