It would be rather foolish, but they can continue using the GBP. Or they can start using the Euro before joining. They wouldn't be able to mint their currency, but plenty of small (often island) nations use foreign currency already.
Scotland is already a separate country, technically speaking, so I don't think it's comparable with the Basque situation. Furthermore, with the UK leaving the EU, they've opened doors that non-EU members can't use to work around such issues.
I don't think it'll happen soon, but the desire for independence does seem to be there to a significant extent already: https://www.telegraph.co.uk/politics/2026/09/13/irish-scots-...
The largest problem for an independent Scotland trying to join the EU would probably be that the EU doesn't just let anyone join. You need to have a strong enough economy and a grip on national debt to join.
I think if you keep researching one of the things that killed the referendum last time was the British government saying a hard no to continued use of the pound while scotland applied to the EU and joined the Euro. Now of course they could keep using the pound, but the amount of economic attacks against Scotland by the City of London and general lack of financial independence seems like it really would kill the idea dead. If Scotland thinks it gets a better deal from the EU than it gets as part of being in the UK then it should go for it but it would be an extremely expensive and fragile 10-15 years in that interim period. And not even full independence, it would be tantamount to saying “we hate the English so much we’d rather be governed from Belgium”.