First off, make a duplicate of the cleaned up Library so whatever happens you have that.
If the Library was created by syncing up with iCloud and it “knows” your library, then reconnecting should apply all the changes you’ve made to the library. it may take some time to settle out, but it should do that.
If you cleaned up a copy of the client’s library then the surest way to replace is to delete everything from the existing photos library and let that sync (delete) from all the devices (of course, the client library is backed up to Time Machine). Then you replace the (old) empty one with yours and replace everything in the ecosystem.