Chances are high that the offspring will be good layers. Body type will probably be intermediate between the two, and if you'd be happy with that, then there ya go.
HOWEVER THIS IS ONLY TRUE for the F1 generation, i.e. the first generation, the ones with one pure Shaver Red parent and one pure BR parent.
If you then breed those mixed-breed chicks to each other, you will almost certainly get a wild mix of whatevers, especially in terms of laying ability. And so on for future generations. Because you'll have thrown together two very different gene pools and no longer have the neatly balanced heterozygosity you had in the first generation, trying to breed those crossbreds onward will be very unpredictable and variable and not necessarily worth your time if you want Results. EVENTUALLY, given many many generations and a large breeding program (multiple pens of a number of chickens) and raising up and heavily culling a large number of chicks, you could re-stabilize them into a new "breed" if you want to call it that, but that would be far in the future. And I'd question what the point would be.
So, it depends what your point is. If you just want decently-performing offspring from the breeding stock that you happen to have available, it'd probably work fine. If you want to undertake a breeding program in the long term, though, it's probably not a real wise use of time or chicken-space IMO.
Good luck, have fun,
Pat