I would just raise a change control to move the validated spreadsheets onto a new machine. If it is just the platform that is changing, e.g the operating system then the spreadsheet can just be reinstalled and point to the same links.
If you are also changing your version of Microsoft Office, which it looks like you are then the level of validation might depend on the complexity of the spreadsheet and whether any of the old functionality that you’ve used still works the same.
I’d probably do a small risk assessment to mitigate any potential risks and do some form regression test as part of the change control test pack.
If your computer or server is being replaced as part of a roll-out, the IT department might have some testing that proved equivalency between the versions as part of their infrastructure qualification - you might be able to leverage that.