iOh i see now, that does seem kind of impossible without hooking the winsock functions, are you able to inject a dll and not get banned?, if so
in the send or sendto hook , you make the connection to the proxy server and send the hooked recv/recvfrom buffer to the proxy and make the hooked recv/recvfrom return 0;
here is a quick illistration
int WINAPI MySend(SOCKET s, const char*buf, int size, int flags)
{
//connect to the proxy
//send buf to the proxy
//return 0; , just return 0 back to send so it doesnt send the original
}