This gave me the cleanest solution, I guess: perldoc perlrun

My script starts now like this:

#!/bin/sh

mydir=`dirname $0`
. $mydir/set_env.sh
exec perl -x $0 "$@"

#!perl
use strict;
use warnings;
# and so on...
[download]

Thanks to all who replied!

Update: In reply to Arge1 below and because I noticed today That I myself needed parameters to my script.

I appended "$@" to my exec above. This will append all parameters, individually quoted, to the exec command for my perl script to handle them.