I think that what you are looking for is a nice light hatchet like the Fiskars X7.
It is a light, inexpensve ($20 or under) hatchet that can chop, split small wood, hammer, and do all of these tasks well. It doesn't have to be the Fiskars, either. Previously mentioned small axes like a boy scout or a carpenter will work well too.
By comparision, a good tomahawk is generally lighter and faster in the hand. It makes for a better weapon, but is generally much less effective at camp chores, often by a pretty large margin. And you will not notice or be able to take advantage of many of the tomahawk's benefits over the hatchet as a weapon unless you have the skills and ability to use them.
Given the physical limitations that you have mentioned, I doubt that you would derive any real benefit of a tomahawk over a hatchet, and a hatchet would be less physically taxing for you to use in a survival situation.