The opposite of su: run a command without root privileges

I would personally invert your strategy and run the script as a non-privileged user, with sudo used to run the commands requiring root privileges. Is there any specific reason you need to run the script as root?

To answer your question however, you can use the -c flag to run a specific command as a user:

su someuser -c "touch /tmp/file"

Reference: http://linux.die.net/man/1/su

I don't want to rely on the hypothesis that a particular username exists on the machine.

There are advantages being the superuser... :-)

scriptuser_created=no
scriptuser=myuser
if ! id "$scriptuser" &>/dev/null
  adduser --system "$scriptuser"
  scriptuser_created=yes
fi
sudo -u "$scriptuser" command1
sudo -u "$scriptuser" command2
sudo -u "$scriptuser" command3
if [ yes = "$scriptuser_created" ]; then
  userdel "$scriptuser"
fi