Replace drain in tile shower floor
I have a tile shower upstairs that has a drain that is cemented into the tile. On the floor below I have ripped out the ceiling and can see what looks like a shower drain that is corroded and it looks like someone may have applied putty to it. There is a very slow drip filling a margarine container maybe once every two weeks. Is it possible to replace the drain in a tile floor. I can easily remove the trap below by unscrewing it from the pipe that is attached to the shower drain. I am not sure how to remove the drain (hitting the small section of pipe that connects to the drain?) Or somehow chipping at the cement around the drain, maybe damaging some tiles and later replacing them? How would I seal the replacement drain? I would love not having to replace the shower pan that doesn't leak as far as I can tell. Thanks
Dennis