I'd go ahead and pack the "dark" suit, always works well for the formal dinners, first one being just a tad more formal than the second one, so you could just bring another dress shirt and be fine for both. The rest of the evenings should be "casual", docker type pants and polo short work well, enjoy!
"we're sailing on the Sea Princess august 3rd to Alaska. would a sport coat and slacks be acceptable for the Captains Dinner , or how about a dark suit ?"
On Princess, "formal" does mean FORMAL. Sport coats are optional on "smart casual" nights, but too casual for formal nights. You probably will see about an even mix of dark suits and tuxedos or dinner jackets, with an occasional misfit in the crowd.
If you have a dark suit, bring it. If not, rent a tuxedo.