But if the OP is building a Mk.1 Cooper he needs the Cooper gear set as well, so might as well look for a complete Cooper gearbox.
I have fitted a Magic Wand Diff cap to a remote style Gearbox Case, mind you, I did have to machine up the flange faces to get them on the same plain. I also removed the dowels from the case to cap face.
Having done it this way, I don't see that it would be an issue going the other way, however, either be prepared to try a LOT of different caps (not easy to come by these days!) or have the parts machined to improve fit. Without doing this, at the very least, expect oil leaks - more so than 'normal'.
Reading the thread, it looks like you're the only one that's said anything about needing a cooper box or building a cooper
