The biggest problem is that nominating another white guy to replace the court's only non-white member (and one who was famous for his role in the Civil Rights movement) looks very bad politically. Clarence Thomas was fairly blatantly chosen on the basis of being one of the extremely rare black conservatives with any judicial experience; I'm not sure who else could plausibly fill that role, but it would be a serious concern.
As for a court without Thomas? It's going to depend a lot on who gets nominated instead. Assuming Bush doesn't screw up and accidentally nominate another moderate/liberal like Souter (and a court w/o Souter would look extremely different, BTW), then whoever was on the court would likely still be well on the right, and thus less consequential on the more hot button political cases where O'Connor or Kennedy is going to be the swing vote. That said, there are some issues where the 5-4 configurations look different than the classic liberal/conservative split (the
Apprendi line of cases being perhaps the best known) where someone other than Thomas might lead to a different result.
Thomas himself has a very distinct judicial philosophy (while it generally leads to similar results, it's arguably quite a bit more sophisticated than Scalia's generic conservative ranting), but it's less clear how influential that has been on the court as a whole.
As for politics? 1992 probably goes more or less the same way; people vote on "it's the economy, stupid," rather than the exact details of who got nominated to the Supreme Court (beyond the generic liberal/conservative split).