We've cruised several times during eurovision and as we do like to watch it have had similar concerns!
On european cruises one of the european channels on the in-cabin TV often has it on - you may have to put up with non-English voice over but otherwise it's pretty much the full Eurovision experience. We watched this year's broadcast this way.
Otherwise the only other way to watch it is to stream - there's usually a youtube stream or similar, but as others have alluded to even with the better internet package this can be VERY hit and miss, especially with the more northerly trips.