It's great to be cautious. I've seen too many guys try to drill and extract exhaust studs and end up ruining the head.
This is my favorite method to remove broken studs but it takes some equipment.
The longer stud should come out with heat, penetrating oil, patience, more heat, penetrating oil, patience, etc. Heat the stud, not the head, vice grips and try to turn a few degrees both ways. If it doesn't budge then apply more heat, penetrating oil, patience and try again tomorrow.
This is my favorite method to remove broken studs but it takes some equipment.
The longer stud should come out with heat, penetrating oil, patience, more heat, penetrating oil, patience, etc. Heat the stud, not the head, vice grips and try to turn a few degrees both ways. If it doesn't budge then apply more heat, penetrating oil, patience and try again tomorrow.