Any roast or sinewy piece of venison will work here, since you are shredding it. If you use a standard roast, the meat will be drier and you might want to add a little olive oil. If you use shanks, neck or shoulder, there is enough connective tissue in those cuts that will melt, coat the meat and make it silky.
This salad doesn't keep well. The meat does, of course, but once you toss everything together it needs to be eaten within an hour or two. If you braise a big batch of meat, shred it and keep it in the fridge, then put together the rest of the ingredients when you want to eat it.