I've seen some instructions recommending using a knife to open up a space between the back cover and trim. Using the dental pick as shown here, it is very easy to break off the screw attachment near the edge of the cover.
I've seen some guides that recommend a technique for prying up on the center of the case. if you do so, it is easy to accidentally damage the battery if you pry in the wrong direction.
When you are reconnecting the camera, be sure to press tightly on the front and back of the connector. Both sides will audibly snap in. If you have only the camera half plugged in when you power the phone, it will damage the camera.
Using the desoldering wick is a good idea. I thought I could heat up the existing solder and pull the wire out but it is very easy to rip off the solder pad if you get the connection too hot.