I very much doubt this - unless Swedish ID cards do NOT include details of the holder's nationality.

The Ryanair T&Cs are very clear - if you are a NATIONAL of a non-EU/EEA country you MUST have your documents checked. This is about nationality, not about residency.

Some years ago Ryanair had a rule saying that you could travel on internal flights on a driving licence, but only if the place of birth on that driving licence was within the EU. They made headlines when they denied boarding to a British citizen whose place of birth was in the USA. Considering how strictly they interpret their own rules I really can't see them allowing a non-EEA national to board without going through the document-checking procedure.

If Sweden issues foreigners with ID cards that don't state the holder's nationality (unlikely!) then the OP may be able to get away with travelling on his Swedish ID card, for the simple reason that Ryanair staff won't know any better. But if the OP's nationality is mentioned on the ID card then I'd say his chances of being able to board without that document-check stamp are close to zero.

As I said... take the train!