I would absolutely not switch to kibble - any kind of kibble - for a 13 year old cat. One thing that every vet I've ever used drilled into my head is that cats, especially seniors, should be on wet food, and that even young ones should receive some wet food every day.
When my cats occasionally threw up, I added a container of cat grass (oat grass or wheat grass) to their feeding area. Usually they would cough up or pass in their stool a hairball within two days and then be good for months. With my last cat, Allie, I made sure she always had oat or wheat grass available.
You may wish to feed smaller meals more frequently, removing the dish after twenty minutes or so. I found this seemed to help minimize any vomiting. Also, to encourage water consumption, put the water dish somewhere different from the food dish - apparently they don't like them side by side. My cat greatly increased her water intake (and therefore her overall skin and digestion conditions) when I learned this several years ago.