Yes, I think jjhepburn has done this - mixed parts from different gearboxes.
From memory, 1st and 2nd synchros are a different type to 3rd and 4th (and 5th where fitted). But I reckon you'll be able to use the 4th gear synchro from your 45 gearbox to fix your 60's third gear synchro. Also I recall that the synchro ring itself (which should have a convex surface on the outside) can be "turned over" (i.e. fitted backwards) to expose an unworn surface.
The sliding hubs and dog teeth (small triangular points) also wear, so it will be a case of assembling all the best parts you can find (it's bound to be an improvement).
Taking the gearbox apart is one of those fiddly tasks with lots of things to get out of order, I think lots of digital camera photos will help. Doesn't the 4-speed also have some massive circlips pre-loaded by cupped washers (Haynes called them Belleville washers) to remove - might be a challenge - I know the 5-speed has nuts on the shafts that are probably easiest to undo with an air impact gun (rattle gun), which is cheap enough these days.
I wonder if there is a FIAT 127 Haynes manual - perhaps the gearbox chapter might be useful to show the disassembly (the Haynes 128 manual had that sort of information, but for a different type of gearbox).
Show us how you get on with some of those pictures

good luck...
-Alex