Two player online game in Flash without dedicated server?

I am new to Flash, but an experienced game developer who made several multiuser games in various languages, but this time I am looking to Flash as the new Actionscript 3.0 seems quite promising... I have almost no experience with Flash coding from earlier though, so please bear with me...

I want to create a real-time two player game in Flash, played over an online connection. Normally, to make a real-time multiuser game you need a dedicated server or similar that will run a socket service for your clients to connect to.

Unfortunately, I do not have money to shell out for this as this is just my hobby project, I only have access to a standard web host with some basic scripting abilities like Perl or ASP, but I am wondering if there is a way to allow two Flash clients to connect directly if the IP address of both are known?

From what I have seen so far, there are some restrictions on how clients can connect. Only to the originating server, or perhaps to other IPs that's listed somehow on that server. The details seem a bit fuzzy to me, would appreciate some advice.

Basically, my idea is as follows:

1. Users connect to my webpage, where a script picks up their IP address and stores it in a small database.
2. Each connected client accesses this database and downloads the current IP list periodically. The list is updated continuously to ensure clients who left are no longer listed.
3. A client can then connect directly to any IP in the list, thus enabling a direct connection to that other client.
4. The game starts, and the clients will communicate everything directly through a socket connection. Making the communication fast (and inexpensive for me :) )...

I am aware there might be some firewall issues here, but besides that, is there a way to have two Flash clients connect directly in this way?

Oh, by the way, I only need to target AS3 clients.

Thanks :)