The Apple and Unicomp keycaps are not going to be swappable, and not even modifiable to make them swappable. The tolerances for buckling springs to work are very tight and depend on the baseplate, the spring and the key caps themselves. At best, you would need to hollow out the Apple keycaps (i.e. carefully drill 104 keys) and stick them on top of the lower part of the Unicomp keys, but Unicomp have switched to single-piece caps, so even that's not possible, and it would have been a long shot anyway because the upper cap on the two-piece Unicomp keys is probably thinner than the Apple keys.
It's been a while since I looked inside a Model M, but I believe you can lift the whole internal assembly (keycaps, base, springs, membrane) from the plastic case. I'm pretty sure it's going to be bigger than that Apple case though which is why you'll need to mould a new case. I think this is the only way you're going to manage this. You could make a white or clear case, and you could paint the base plate in white too, which leaves the colour of the keys. As far as I know, Unicomp BS keys have only ever come in PC beige, silver with sparkles and plain black. The PC beige keys will give you that "yellowed in the sun Apple keyboard" look, but I think the black keys will look smarter against a pure white keyboard (no labels on them though).
It seems like a lot of work. If you're going to tackle it, good luck to you, but seriously, the Matias TP 3.0 is likely to give you what you're looking for.
