1) You do not need to store the full blockchain - you have a choice how much you want to keep, but indeed - it will try to download the whole history.
2) You may open your wallet in Bitcoin Core (even in offline mode), export private keys (
https://bitcoin-rpc.github.io/en/doc/0.16.0/rpc/wallet/dumpprivkey/) and then import into more 'friendly' wallet, like Electrum (
https://electrum.org/#download)