You will require assistance and a lot of trust from your system administrator. Ordinary users are not able to run the executable of their choice on behalf on other users, period.
She may add your application to
/etc/sudoers with proper settings and you'll be able to run it as with
sudo -u nobody. This will work for both scripts and binary executables.
Another option is that she will do
chown nobody and
chmod +s on your binary executable and you'll be able to execute it directly. This task must be repeated each time your executable changes.
This could also work for scripts if you'll create a tiny helper executable which simply does
exec("/home/you/bin/your-application"). This executable can be made suid-nobody (see above) and you may freely modify
Hope it helps,