As I have managed to run Age of Conan through proxy from the place where only basic ports are allowed, I think some people might find this solution useful as well. There could be some more elegant way how to do this though, especially with the patcher. I'm no IT guy.
You will need two programs: HTTP-Tunnel and Proxifier.
Download and install HTTP-Tunnel, free version is good enough for solo play (bit laggy), don't try raids or groups. However, Proxifier is commercial app.
HTTP-Tunnel
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Just run the app, nothing more.
Proxifier
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1) Go to Options and choose Proxy settings.
2) Click Add, address 127.0.0.1, port 1080, SOCKS version 5, OK
3) Go to Options again and choose Proxification Rules
4) Click Add, choose rule name, and Click Add and find Ageofconan.exe, OK. (I didn't manage to run patcher with Proxifier, but since patcher runs fine without it, I have just run Proxifier after the patcher finished its job.)
5) Go to Options again and choose Name Resolution.
6) Uncheck Choose the mode automatically, and choose Try Locally then Remotely.
Now we are done with Proxifier, and we will edit hosts file. The hosts file is located in C:\Windows\System32\drivers\etc. Open it in the Notepad and add line: dm10-nj4.ageofconan.com:7000.
I hope it helps.