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.
To pickle the onions, slice them thinly from root to tip and soak them in lime-orange juice mixture while the venison is cooking.
Mix all the ingredients for the braise together, bring to a boil and simmer gently until the venison begins to fall apart. When it’s tender, shred it with two forks and toss it with the salad ingredients. Garnish with the onion and radishes. Serve on tostadas or corn tortillas.
Notes
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.