Remember when syncing a library that yes, the record numbers will change.
Usually you would make sure to update citations and bibliography then move the document to the other machine. Then open the synced library and first update citations and bibliography in the document. This will match the citations, record numbers to the local library.
If you unformat the citations and then move, yes the citations will miss-match. Go back to the original machine, update citations, move the document and update once again. If that is no longer pssible, you will have to match the citations.
You will have to go through them all, save and backup the document. Always have back-ups of your library and Word document as you work.