As I said I'd keep you posted on any update, here it is :
I still haven't figured out why the hell my app would stop if it wasn't launched with the console. I doubt it's related to JIntellitype, but since it only happened when I used it, I'm still noting it.
How I fixed it : I wrapped my .jar in a .exe, and now it runs without any problem and without the console.
Good job again on this useful library! and happy holidays!