not really sure how this goes, I think a lot of it depends on conditions of the match i.e where they meet and so on
If they are in a neutral setting, then GER should win. It can nullify the Shrike from actually using any of its abilities or jumping through time to begin with. Additionally the death loop just requires contact (unless JoJo a GoGo translations coming later this year change that) and during the death loop your actions are still nulled. Diavolo could have cancelled out of any of the deaths he experienced but wasn’t allowed to do anything. Current english translations are explicit in that what Diavolo does when he destroys a piece of time is universal, and GER doesn’t have any issue reaching other spaces and so on.
However, while GER can affect things retroactively, there isn’t really any indication it can freely manipulate the past at all, only the present and future. So if the Shrike is actually able to move back and so on I don’t know what GER could do about that.