Here is a link to the train schedule.

http://www2.jrhokkaido.co.jp/global/english/ttable/04.pdf

It looks like you can take a train from the Sapporo airport directly to Otaru without changing trains. A poster on TripAdvisor (who coincidentally is on our cruise - she was on our Silversea Arctic cruise last summer) posted the following:

We have caught the train from the airport to ShinSapporo with luggage and it was easy. We are both in our 60s. We had two large suitcases and two carry on bags - all had wheels. There is a lift to the platform, luggage storage section on the train, we had the booked seats section. There is an announcement on the train what the next station is, so you can be ready to get out. Make sure you have your hotel name written in Japanese as 99% of taxi drivers do not speak English. We travel to Japan every year, use the train to get around and have not had any problems. Later this year we are also going on a cruise from Otaru port and will be getting to the port by train and taxi.

We took a train to and from the Osaka airport to Kyoto a few years ago. I was a bit apprehensive ahead of time - especially about signage and announcements - but it was a piece of cake.

We will most likely do this and stay in Otaru for the two nights before we board.