I need to transfer fiat currency (EUR or USD) between two exchanges.
This is where the stable coins come into equation. Right now Tether is on down trend because of issues and many others started to fill the market. Find something that is accepted by both exchanges and you are just fine.
GUSD may inspire more confidence, but I don't know if many accept it for now.
If you don't do this for arbitraging (normally such transfers are for arbitraging, but if you wait 3 days for transfer maybe you do something else), if you want to make the transfer in "quiet" market, any major coin would also do the job.