If Shavo wanted an oak wing TBird and Gibson wanted his name to grace a signature model, they would build him one no sweat.
If you read about oak as a potential tone wood, you hear all kinds of things: too heavy, too fissure prone, too narrow a frequency spectrum, "unremarkable" sounding, "too short-fibred for good sustain and resonance","though over-abundant it was never used for instrument building in the Old World so there must be something wrong with it for acoustic instruments at least", "Brian May's guitar is made of oak and sounds fine", "I know someone who built an oak Jazz Bass and it sounds great, kind of like ash", "premium quality drums are built from oak, so it can't be that bad as a tone wood", "requirements for a drum wood and a bass wood are totally different".
Given that we are only talking about the wings of what will still be a maho/walnut neck thru structure, I don't see anything that would rule oak really out should Shavo want it. Weight doesn't seem to concern him much as the enlarged headstock and vintage open tuners of the model I saw evidence. He probably just wants a TBird he can beat the shit out.
The Shavo model I saw was very handicraft/robust looking: The headstock looked plump and rough, the open tuners strangely old-fashioned, the silver-grey fin all streaky and the wood of the wings beneath that streaky fin plain. In contrast, the Nikki Sixx model hanging right beside it was a real eye catcher, but then this is Nikki's/Gibson's second (third, if you count the Epi) attempt at it!
Uwe