Probably FXSAVE or XSAVE for the mathy registers, yes. But that doesn't cover the general purpose registers, and (F)XSAVE can be skipped if the process in question doesn't use fancy math (easy to detect, disable it, when the process uses it, the kernel will catch the fault, then enable it and set a flag on the process so it saves and restores that state as well)
Wouldn't Windows (and Linux) use the FXSAVE instruction instead?