I would avoid using your king for any island invasions, regardless of the state of your navy. Your invasion will most likely destroy the province's port, which will strand your king for at least 4 years, and effectively cut him off from the rest of your lands. For land attacks, I will use my king sometimes when my empire is small, but I find it better in the long run to get stars and virtues on my heirs. Groom them early and often.