I'm no gun smith but what I do when I remove the pin/spring then there is no pressure on the bolt then it moves freely unless the brass shoulders start rubbing inisde the chamber. Just the way I've done it. Would this tool do the same ?
Sorry, just don't know about Cooper. I do note though that Kleinendorst has a couple of different bolt disassembly tools besides the Rem 700. And the Cooper bolt pics I see are three lug so the Rem ejector tool probably wouldn't work.