finding out which files have been updated after a cumulative update

I can't make a recommendation as such as I've never tried doing that.

Registry snapshot tools are typically intended to compare small and limited changes. E.g. before and after program installation.

Generating the comparison takes quite a little while. In your case prepare for a mammoth listing.

You'd be looking for one that can save the snapshots, then retrieve the first after a restart for comparison.

I'm not sure Regshot can do that.. there are others e.g. perhaps this one (never used it):
RegistryChangesView - Compare snapshots of Windows Registry

The description seems to suggest it could do that.

For more, simply search e.g.
compare registry snapshots freeware
etc