Oh, that explains it. I guess, if you really needed you could construct something like "Jestem w trakcie (kogo? czego? so genitive, indeed) żeglowania (kim? czym? instrumental) statkiem".
"Żeglowanie na statku" is a tricky thing, could be understood instead as if there is a big pool on the ship and you are sailing(using some very small yacht, probably) in that pool – to avoid this ambiguity "żeglowanie statkiem", "żeglowanie yachtem" and so on is a better choice. ;-)
I wrote "we are on the boat", and it was accepted, but now I'm wondering, these two sentences being very different in English, do they really translate the same in Polish? Example: (We are stating our current location) -> We are on a ship (We are letting friends know (by phone or letter) that we are on board a ship for the next stage of our journey) -> we are on the boat. Just curious :)
This is how I would express it: - First, the difference between boat and ship: a boat is any water craft, regardless of size. A ship is a large water craft used for transporting people (or naval warfare). For example, a fishing boat, but a cruise ship. - Second, to be "on a ship" is to be physically located aboard a ship. To be "on the boat" is to have come aboard some sort of water craft in order to go somewhere. Examples: - "It is restful to be on a ship in the ocean" - "We are on the boat, arriving in 10 hours."
I think the use of "the" versus "a" means that either the boat has been mentioned before, or it is part of a trip from one place to another and then the previous mention is included in subtext. I don't know if this makes sense. It works the same way for plane, by the way "on a plane" means aboard an aircraft, "on the plane" means embarked on a flight to some place. Unless the specific craft has been mentioned before, using "the" implies the existence of a plan to travel.
OK, so firstly, we accept "boat" because it's a word with a very broad definition, but an equivalent word which also can be used for any water craft is "łódź". "Łódź" is also one of the bigger Polish cities ;)
A ship should be translated as "statek", but there is also "okręt". Okręt should be an army ship, but it's quite possible that many natives can be unaware of it and try using them interchangeably.
About "a"/"the", I don't think there's a difference in Polish simply because of the lack of the a/the difference. Perhaps you could put "na pokładzie" (on board, aboard) somewhere if it's useful in a given sentence.