Cassettes almost always wobble, because the freehub/freewheel's axis of rotation isn't exactly aligned with the wheel's axis of alignment. Unless the offset is big enough to mess with shifting, it won't affect the ride in any way.
Changing the cassette won't fix the problem. If it's really bugging you you'd have to change the hub or the freehub body (or the freewheel) and simply hope for better luck with the next set of parts.

But it is possible that the the cassette isn't quite tightened down on the freehub body, in which case tightening the lockring up might improve things.
I have no idea what you mean by "tiny backlash".