Xastir is most likely what you want. http://xastir.org/index.php/Major_Features#SUPPORTED_TNC.27s:_DARN_NEAR_EVERYTHING.21
YACC - Yet Another APRS Client is also a newer choice. I have not personally tried it.
You could use Aprx or Direwolf and configure the client as a Receive-only iGate. You can then assist in sending some directly received data to APRS-IS (the Internet side of APRS) and see the data appear on sites like www.aprs.fi
You will need a password to be able to log to aprsis but this is trivial once you have a callsign and google for aprs password ...
You need the applicable reverse-polarized TNC adapter. Sounds like you have a standard TNC Female on your antenna
and a RP-TNC Female on your device.
Can you confirm?
Based on your comments I'm concerned that you are not certain of your determination of the existing connectors. (It's easy to confuse standard TNCs with ...