restarting a airport from the commandline - of a non-mac
You're asking a lot of different stuff here.

Here's the question I am going to try to answer:

"How can I bring my Airport devices into my Nagios monitoring more closely?"

OK so first of all, Nagios supports SNMP and (most?) Airport devices support SNMP.  So "all" you have to do is configure the Airport SNMP settings and then set up Nagios to ingest the data.

Unfortunately the current version of the Apple's Airport Utility (6.3.1) removed the interfaces to the SNMP settings in the Airport.  You can still download the old version (5.6.1) from Apple but the installer for the old version of the Airport Utility refuses to run on Mountain Lion! However it turns out that it is only the installer that is broken in ML!

Some crazy genius has written and made available an Automator workflow that works around this and allows you to install the old version of Airport Utility.  I just tried it and it worked.  Was then able to use it to set the SNMP settings of my Airport devices.

If this ends up working for you and you accept my answer, you should consider rewriting the question so that the question and the answer match.