UPDATE!

Instead of using the registry association of my script, I wrote a .BAT file that receives the dropped files in its icon and then it calls my perl script with all the received parameters (files):

But I found something interesting: the working directory for the scripts was the source dir of the dragged files!!! I was expecting it to be the same dir where both the .bat and .pl files were located.

I didn't hardcoded the paths in both script files. What I did was to create a shortcut to the .bat file. This allowed me to do two things: (1) Set the path of the working directory in its properties, and (2) change the icon to something that could be identified... I chose the pointing down arrow usually used for "download".