How to recook a roast?
Stewing tough or thoroughly connective-tissued meats is, by design, something you do for a long time at pretty decent temperatures. Since your meat has already been cooked once, if anything you are going to be cooking it slightly less than what is described in whatever stew you decide on. Your food safety concern is admirable, but as long as you observe good food handling safety and cook the meat thoroughly, you should be good to go.

I will reiterate the chat's suggestion for a stew as a good one. However, a stroganoff (which is an American version of an Eastern European dish, I believe) would also be a good option. Basically any beef dish where the beef is diced up evenly in size and stewed in a sauce for a long while will work in helping you to use up this meat.