I haven't tied on bitcoin core yet. Will it work offline if import private key. Back in 2009 all I had to do was type the private key and add 5 in the beginning. It used to work back then.. I will try and see if it works once again
It would work if your bitcoin core is not pruned or if it's pruned mode you must disable it before you import.
Here's the way to import it
First, make sure it was not pruned mode enabled to check that find the bitcoin.conf or go to settings just uncheck it on the settings or remove prune=x from bitcoin.conf.
Next, go to console and use this command.
importprivkey yourprivatekey
If your wallet is passphrase protected you will need to type this command first before you can able to import it.
walletpassphrase mywalletpassword 60
Then use the import command again
Take note it won't show any balance until your bitcoin fully sync and rescan.
For me, If you want to transfer the balance of your old wallet right away the best option is to import it to Electrum if it started with 5, not K or L then you will need to convert it using bitaddress like what I said above.