See your Ops Specs?
The Ops Specs for my company specifically list "Departure Priorities."
For Engine-Out, the priorities are listed as:
1. Special Pages for engine-out departure
2. IFR departure procedure (Obstacle DP)
3. straight-ahead until flaps retracted or safe maneuvering speed is reached.
In following these priorities, and with an engine failure departing LSZH runway 16 using the WIL 1R, I would advise ATC that I would be following my company's special engine-out departure procedure, which they have a copy of. The procedure abandons the WIL 1R, taking an entirely different route.
The engineering dept has worked up similar procedures for each airport where E/O performance required further analysis. It allows operations at higher weights, and this means more money. Without this info, one would have to determine if aircraft performance would allow an acceptable level of safety at a particular weight.