I think Iceland will find that compliance with the EU regulations would be very expensive and not practical, but that’s for them to decide.
Iceland is in EEA. EEA is already EU-lite, where they have to comply with plenty of EU regulations, don't get a vote on those regulations, but get some exemptions (such as their fishing thing).
Other two countries in EEA are Norway and Liechtenstein.
The presence of EU across the sea is making their exporters to comply, same goes for UK. Does not matter if you are a member or not. You can either comply with the roles or not export to EU.
They're in the single market already.