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It is 'normal' to take the Pool Towels ashore on Celebrity & every other cruise line, however I believe in Concierge Class an additional Beach Towel was provided. Whatever the case I wouldn't bother packing towels as there will be towels to take ashore for your pleasure.
Found the following on the Delta website.
All Delta passengers are allowed one carry-on bag and one personal item that meet the criteria below.
Size and Weight Restrictions
If your carry-on bag doesn't meet these size and weight restrictions it must be checked, and all checked baggage rules will apply. Your bag must:
Weigh less than 40 pounds (18 kg).
Not exceed 45 inches (length + width + height).
Fit easily in our SizeCheck® unit (approximately 22"x14"x9").
Fit in an overhead bin or underneath the seat in front of you.
You're allowed one personal item from this sample list:
Purses, briefcases, camera cases, and diaper bags
Laptop computers (can’t be checked and must be carried on)
Items of a similar or smaller size to those above
Hope this helps.
We were on Mercury the sister ship of Galaxy and we did have beach towels and it seems to be an item listed on their website but perhaps others will comment. On hand luggage your case meets the Delta allowance which is 56 x 36 x 23cms so no problem there. The Galaxy is a lovely ship we sailed on her in 2007 in the Caribbean starting of from Puerto Rico. We flew home via Boston which was in the middle of a bad snow storm, but the plane landed despite this but we were stuck for 3 days before we got a flight home, it was unfortunate it was the St.Patrick's Day week-end and finding a hotel was a nightmare but we got one. We still nevertheless enjoyed our cruise.
I bought the m&s small value ABS hardcase last year to use as carry on to avoid checking luggage for short trips, same dimensions as yours, and so far have had no trouble on Virgin,BA and US airlines. As it seems to be an international dimension ruling, you should be OK.