Order of operations to rename linked files

I am responsible for maintaining a 1000+ page manual with several hundred numbered exhibits, some of which are PDFs placed into InDesign and some of which are tables within the InDesign file. The PDF files are named according to their exhibit number. This makes perfect sense until a new exhibit gets added or an existing one is removed and all subsequent exhibits from that chapter section must be renumbered. I have accepted that there is no way to automate this process, since the numbers aren't even sequential (since not all exhibit numbers have a corresponding PDF file in the links folder).

Given that I need to manually rename a bunch of PDF files and then update the links, what is the best order to do this to minimize the chances of accidentially having a frame get relinked to the wrong exhibit or accidentially resized or shifted within the frame somehow? There isn't any way to directly rename linked PDF files from the Links panel in InDesign, is there? I am thinking I should rename the PDFs one at a time in reverse order while I have the InDesign file open and relink each as I go along. Will this work?