Use the gym and SWIM in the pool on board......every cruise liner nowadays has at least a small pool...larger ships usually have huge indoor and outdoor pools. All you need to make sure of is that you use it and swim swim swim.
Most cruise liners have buffets and you will be able to pick and choose. If you are on a big ship from P&O Lines for example like Oriana, you will be spoilt for choice for food, the breakfasts are AMAZING and will set you up for the day (make sure you load up with eggs bacon, ham, and all the trimmings). Dinner in the evening will always have a choice of good cuts of meat and veg, so just have lots of that and cut out the things you don't want like potatoes and bread products.
On shore, you can head for the local eateries and try some Mediterranean food which is great - and there will be so much choice in the way of meat especially SEAFOOD which will be inexpensive and straight from the sea that day. In fact, you could eat wonderful fresh seafood every day alone and remain 100% paleo without much effort.
Things may get a little trickier in Egypt if you are going along the Nile, but there should still be wonderful fish dishes on offer and you will also be able to find spiced meat dishes which are usually delicious, the trick is to get deep into the souks and taste the LOCAL cuisine. You want to do that anyway, hey? ;)
I have found that the staff on cruises are always on hand and very ready to prepare food in the way you want it, and here in Europe staff care very much about how food is served to the customers, even if you stick with meat alone, you will find that they may be able to prepare a different sauce for you, offer you a different vegetable option and cook the meat exactly to your liking. I think you will be OK!
Have a great trip.