Thinning out Black Bay 41 shield version thickness by swapping caseback?

[Duckber]

I'm thinking of buying both the shield and the rose version of the Black Bay 41. Shield version has a better dial but is very thick. From what I understand, the thickness of both the cases themselves are the same on the shield and rose. It's the caseback extending outwards on the shield rep that makes it thicker.

I am curious if the caseback on the rose can be put on the shield to make the shield the same thickness as the rose version. I'd sell the rose version after modding the shield.

Is this possible?