P.S.: The chainsaw shell script is not executable by default on Linux. I have no knowledge of maven scripts so far, but it might be just a small change to include this?
The appassembler plugin for Maven does not provide that feature, which I believe is due to the fact that Java itself cannot set that flag, because not all O/S support the concept of executable. Only a very recent version of Java actually exposes an API to tell if something is "executable" or not, yet still there's no way to set it I believe.
Details (the lacking of options) are here: Appassembler Paul