Well, as you probably read in the waterwiki, disassembling it in full (at least including step 7 here: Fairphone 2 Teardown - iFixit) is always the best recommendation.
Now with regard to the display, if you have the opportunity to test someone else’s FP2 display on your device, that would be ideal (although unlikely, I guess).
If you need to access the data on the phone, you might want to get yourself an OTG adapter that allows to connect a computer USB mouse with the FP2 – this should allow you to control the screen without touching it.
P.S.: There is a Fairphone Angel in your city. Maybe s/he still has an FP2 or FP2 parts to test on your device.