The original skewb mechanism is actually somewhat unusual. Just like a 2x2 usually has a 3x3 inside of it, the logical mechanism for a skewb should have a master skewb inside of it. That way, none of the corners are actually attached to the core, but are instead extensions from the corners of the master skewb. Of course, this is much more complicated than it needs to be, as we all know from looking at the mass produced skewb.
However, that may be the best way to go about making the Mixup Skewb, since it would guarantee that all the corners have the same mechanism, so they can all be interchanged, as this puzzle seems to require.
P.S. You have a Shapeways Shop yet? You have a ton of get ideas... you should be putting these up on Shapeways. In this case that is another way to answer your question. If you can design this puzzle with either type of core, since its never been done before, I'd thing the only way to be 100% sure which was the best would be to try both. Shapeways enables that type of prototyping.
Seconded. I would love to see some of your puzzles in physical form. PM me if you want help preparing any of your designs for Shapeways.