I like to think of hyperspace as somewhere else entirely. Another dimension where the positions of stars are jumbled in a hyper-dimensional space, and we are really moving orthogonally to normal minkowski 4 space to get there.
I think of it in similar terms: something like an alternate dimension, where the speed of light is well below the speed limit, and those aren't even stars and nebulae or whatever that are wooshing past, but some other-dimensionly Things.