Workbook feeding Word doc: change SheetName for all links in Word doc

I think my title says it: I have a workbook with one Worksheet that during Testing I named "1st Bienium" and now realize should be the only sheet used, so want to rename to something more appropriate like "Update Page". The issue is the worksheet has 68 different cells feeding 68 links scattered throughout my Word doc (a 6 page letter). These links aren't in tables, so each one is a unique stand-alone link that took a while to set up.

In Word, when I go to File, Info, "Edit Links to File", "Change Souce", the prompt is to select a workbook, and I'm afraid that when I do that I'll have to select the worksheet and cell location for each link. How can I simply change the Worksheet Name in all of my Word links?

Thanks Macropod and Tinbendr. Sorry I couldn't replay sooner. Your solutions worked wonderfully!