I'm a Royal Caribben cruiser. While I have seen the policy enforced on longer cruises, I can tell you that the dress code is a lot more lax on the 3 & 4 night cruises like the OP's. It's just a completely different atmosphere on those cruises than on other cruises. So it is possible that the staff may allow shorts in the dining room on the OP's cruise (even though the stated policy says no shorts). But since it's not a definite he does need to throw a pair of pants in his bag.

Crazyhotelguy, yes the policy is different on other lines and enforcement levels can even vary among ships. Some cruiselines even have rules where you can't use most of the public areas after a certain time in the evening unless you are dressed up.