I have been to Alaska several times and shot from boats on every trip (although I have never been on a cruise ship). This is a once in a lifetime experience for many. You will see lots of wildlife--whales, eagles, bears on the shore, all as you expect and maybe even more so! However, distances will be long and you can expect overcast weather much of the time (you might get lucky but be ready for cloudy and even rainy/sprinkly weather).
I will assume that you do not want to really shoot much at 1600 or above and are looking to tap the better image quality in the ISO 200-800 range.
For shipboard shooting I would most definitely recommend a zoom as your subjects will be at different distances and often moving (whales, dolphins, eagles in flight etc). Also, I would recommend IS as pretty essential. I definitely not leave your 45-200 behind as you might find it essential for much of your shooting.
You have an excellent longer option with the Nikon 70-300 and you really do not need anything else. Why spend the money?
If you truly want the best range of longer focal lengths, probably the ultimate choice would be the Sigma 50-500 zoom. It is larger, heavier and more expensive, but there is nothing you will encounter that that lens will not cover from the ship and with very good quality.
For probably the best image quality, but with a loss of flexibility, I would also vote for the Canon (or Nikon) 300mm f4. You get 600mm equiv. with wide aperture for fast shutter allowing lower ISO. Can use a teleconverter for 420mm (840 on m4/3!!) and still have 5.6. Again, care in technique is essential and the 840 length may be unuseable much of the time. A shorter 250 makes no sense-- only 20% more magnification over your already good 200. To make a difference, add a 300.
But, remember that without IS, any focal length 300mm (600mm equivalent) or over is going to be difficult to impossible to use. Even though a ship is stable, I suggest bringing a monopod which you can also brace against the ship's rail. This will give you worlds of improvement over hand-holding and make the difference between once-in-a-lifetime quality shots and blurry snaps.
Whatever lens you choose, at least consider adding a polarizing filter which will make a significant improvement when photographing into the water.
I would NOT get any mirror lenses. The focal lengths suggested (350/500) are 700 and 1,000 equivalents and you will not be able to handhold them or even monopod them and get reliably decent results. Their bokeh is atrocious and that really shows in wildlife photos. If you are photographing over water for whales, birds and such, the out of focus highlights in the water will show as donuts and are very distracting, and even dark backgrounds are busy and unpleasant looking. These lenses can be very sharp but their contrast problems cause loss of detail. They are niche lenses for ultra-portable ultra-telephoto lengths, but not real contenders in terms of image quality. You cannot use a filter on most them and even if you could they are too slow to allow a polarizer.
To sum it up:
Bring your 45-200 with IS!
Best zoom combo to reach 600mm equiv--add your Nikon 70-300 and no more cost!
Best extreme-range option: add the Sigma 50-500
Best image quality: add the Canon/Nikon 300mm f4, with 1.4 converter if you want.
Monopod essential.
Polarizer recommended.
Hope this helps!
Guy
