Hi @Marcel_Jackisch. The solution you described should also work for Hardhat.
I would recommend doing a deployment of a UUPS proxy for your existing contract to Hardhat Network (i.e. locally), and then copying the generated .openzeppelin/unknown-31337.json file to .openzeppelin/mainnet.json, replacing the relevant addresses (impl and proxy) for your addresses on mainnet. Then you should be able to run the upgrade based on that file.