Greetings cwilson,
Khomas Highland Hunting and Fishing Safaris of Namibia, welcomes you to the greatest forum on earth.
I’m with others here who have already suggested low recoil cartridges such as the 7x57, the .308, .30-06, etc.
That said and regarding giraffe specifically, I’ve never shot one so admittedly, my opinion is probably not the best one to consider.
Certainly, I have seen many of them (7 times to Africa so far) and they are huge.
I think a mature bull weighs around one and a half tons.
And their bones are massive.
Therefore, selecting a low recoil cartridge for the shooting of such a giant critter is going to be a challenge for sure.
My best guess here is that if your wife can tolerate a .30-06 with 220 grain bullets, and she is able to (from shooting sticks), consistently hit targets representing the juncture of a giraffe neck and base of the skull, then that is the caliber I would suggest.
As for zebra, the .30-06 and 220 gr bullet is adequate, of course just like anything else, provided the all-important first shot strikes a vital spot.
Best Regards,
Velo Dog.