The easiest way to do it is on a repositioning cruise where at the end of the season the cruise lines take their ships from one market to another. The positives are a cheap cruise, the negatives are that you're right at the end and beginning of ideal seasons so your experience at each end might not be great. Also you'll have a lot more sea days and fewer port days which could be in either column.
Weather at sea can be considerably worse than coastal weather. Cruise ships are pretty stable and it's unlikely to be awful, but plenty of people do get seasick. I used to be a professional sailor and so obviously can't see what the fuss is about, but probably half the passengers I spoke to felt ill on at least one of the days, and a few people spent the entire ocean transit in bed. If you're prone to motion sickness take some medication with you.
The atmosphere is different to regular cruises. Typically less of a party and the clientele skew towards older and more independent travellers.
To answer your actual question - go to cruisemapper and seascanner and you'll find them easily enough. They're all over the world.
Yes exactly repositioning cruises ! I confirm what you're saying. Sometimes you also get people who were visiting a continent going back home. For example Brasilians going back home in December for their summer
Modern ships built in the last 10 years have stabilizers. I've been in a big cruiseship without stabilizer before and it can indeed move a lot laterally up and down (in the directions orthogonal to the direction of the ship). So, for people afraid of that just research if the ship has stabilizers
Weather at sea can be considerably worse than coastal weather. Cruise ships are pretty stable and it's unlikely to be awful, but plenty of people do get seasick. I used to be a professional sailor and so obviously can't see what the fuss is about, but probably half the passengers I spoke to felt ill on at least one of the days, and a few people spent the entire ocean transit in bed. If you're prone to motion sickness take some medication with you.
The atmosphere is different to regular cruises. Typically less of a party and the clientele skew towards older and more independent travellers.
To answer your actual question - go to cruisemapper and seascanner and you'll find them easily enough. They're all over the world.