thanks for the hint … so the solution is much easier. :)

Drop all changes from /etc/sudoers and remove /usr/local/bin/nagios-check-apt-updates.
Exchange “/usr/local/bin/nagios-check-apt-updates” with “/usr/lib/nagios/plugins/check_apt” in /etc/snmp/snmpd.conf and search for “APT OK” in the response of check_snmp.

you know that there’s a check_apt in nagios-plugins, don’t you? :)