Take off the trim surrounding the door. The hardware for the door is behind the plaster on the wall. You will find it level and to the left and right of the respective door's top. You'll have to knock out the plaster and cut the lathe to get to it.
The doors are likely very heavy and I've found that by supporting the door, the removal is easier.
As for the structural integrity, No - you won't compromise it. Its a safe job , but you'll need help.