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Surely Princess provide this info. China most certainly and costs £40 approx, Russia - all cruises say you can only go ashore if you do the ships tours - but this is not strictly true. If you arrange private tours via companies like Red October you will be taken care of under their blanket visa scheme. Korea - no, Japan - no and Alaska is part of the USA so you will enter under the visa waiver scheme.
It cost us 190pounds with P 0 for 2 visas to visit 2 ports in India and because my husband has an republic of Ireland passport he had to send a utility bill 12 months old (he's been living in England for 52 years) China will cost and also Russia.