Your question does not really make a lot of sense as asked.
It is technically possible to do this, however it is an extremely advanced technique - this is something I would find challenging to pull off - and I have years of experience in this field. The practical answer to your question, given the level of knowledge implied in it, is no - you can't do this.
Exploring how an expert might do this on a server (probably a Linux based machine so you can more easily access the raw components and chain the use of tools to do it) -
The key stumbling block will be identifying open networks and making connections. The easier way would likely be to generate a list, then write some code to associate the accessible IP addresses with ports.
(A more elegant, but very hardware-dependant -but near impossible way to do this would be to simultaneously connect your router to multiple SSIDs, and then assign those SSIDs to ports - this would allow the use of more then 1 proxy at a time)
You would then need to run some kind of proxy/cache subsystem, along with policy based routing per SSID to route the requests. You would probably need to configure multiple instances of a light-weight proxy servers for various ports, or a single proxy server and bind it to multiple ports or use IPTables to do the same.
You would likely need to monitor the ports and modify the outbound connection depending on the port - conceivably you could use a hook in the proxy server or a frankenmonster configuration of Fail2Ban to assist with this. (If you can somehow connect to multiple networks you could likely avoid this step)