I just bought a pair of SRAM Powerlocks for 10-speed chains. The packaging says that they can only be used with SRAM chains. Will anything nasty happen if I use it with a Shimano chain and cassette?
They will work fine together- same if you swap the brands around. I've done this many times for myself and for others with no issue and it's common practice amongst bike shops. This is strictly marketing & legal covering of their own asses. If you look at Wippermann Connex Link compatibility they say that the one link is compatible with SRAM, Shimano, and Campy. They're all so close in terms of the spacing that interchanging their quick links doesn't make a difference.
As an aside, those Wippermann Connex quick links rock. Tool free installation and removal, and it's almost impossible for them to come undone while riding.
I don't recommend doing so. I put a sram powerlink onto my shimano chain, but it was so tight that the chain was not moving smoothly back and forth. And because it was so tight I couldn't get it off again. I had to use a chain breaker and physically destroy the link.
Instead, I recommend the KMC quick link, these seem to be much more compatible with Shimano 10speed chains. I've used a bunch of them in the past.