The replacement went smoothly ... but was pointless :-(
My MacBook Pro screen gradually turned black (in fact, not totally black, but no graphics anymore). At first it could be revived by yanking the edges, but finally it didn't light up at all. I decided to replace the screen data cable, because it was the most obvious (the macbook worked well with an external screen, and the data cable was the cheapest repair option).
Thanks to the ifixit illustrated guide, the repair went smoothly. Unfortunately, after having reassembled everything, nothing had changed. I suppose I should have gone to the LCD replacement, but the price tag was a bit of a drawback for me. Anyway, I'll keep the MacBook as a-very small form factor-desktop.
A colleague of mine gave me this advice : use some plastic cups to keep all the small parts step by step. you can pile them up after each step, and they will be in the right order for reassembly