For bitcoin there is Bitcoin Core which downloads the whole blockchain a few hundred gigabytes then you can use the wallet.
Any help how to get access to a wallet using the backup keystores from the "old"/"classic" wallet?
What you mean is this
https://github.com/ethereum/mist/releasesI do not really understand the classic node wallet ethereum, but please examine the link above. I'm just giving an idea, danger or not, maybe you are more aware because I haven't tried it myself. Sorry if i wrong about that.