I strongly believe there should be no immigration check if the only stopover is Alaska as it is US territory. I had been to Hawaii with expired H1B and there was no immigration check for flights inbound and outbound from/to the US mainland with not other international stopovers (direct flight).
Just like the airplane travels over international airspace, the cruise is travelling over international waters but do not have any stops at international ports so immigration check should not happen.
It is always best to call and check with the cruise company.