If ABSOLUTELY limited to either a .223 WSM or a .243 WSM, I'd definitely go for the .243 WSM.
However, a better choice might be something having light recoil, but with more bullet weight making it a better, lighter recoiling rifle/cartridge combination for deer than the .243 WSM.
The larger (7mm & up) calibers could double as a reasonable elk, black bear, caribou and even moose rifle/cartridge under most circumstances for those hunters who occasionally mix the larger game with their regular menu of venison.
Some that come to mind for deer would be the Savage 250/3000 or the new .260 Remington and, for game larger than deer, the famous 7mm Mauser (7X57) or the excellent .300 Savage... all of which are within a woman's "kick" tolerance (15 ft/lbs & under).
Something to think about, my friend...
Strength & Honor...
Ron T.