Well, first the party line : you should not undertake repairs without landlords approval. What happens if "something happens"??
Now, without seeing the water flow, it is hard to advise. If I were to try this, I would do a couple of things:
Have all new parts standing by.
Run kitchen and lav faucets wide open to reduce water pressure.
Open hot and cold on tub wide open before removing.
The biggest potential for damage is that when you remove the stem, water will dribble or pour out of the body, and run down BEHIND the tile or fibreglass walls. You can have a bunch of plastic bags and towels ready to stuff in there, to direct the water out into the tub/
My best advice is to talk all this over with the landlord in advance. Tell him you would like to fix the shower, but the water is running. Discuss the pros and cons. Maybe he will work with you and turn off the building for half an hour.