Route teamviewer desktop client through SSH tunnel in PuTTY

I'm trying to route the TeamViewer desktop client through an SSH tunnel I've made using a home server (with DD-WRT) and PuTTY on my end. In PuTTY, I chose port 1080 to Dynamic range, so it works fine and dandy as a socks proxy in my web browser.

However I know SSH is for more nice stuff. I managed to use socat thanks to someone else who helped me here on this group for routing GMail's IMAP server to my Outlook client, but alas, IMAP and SMTP/POP3 servers are well-known. Teamviewer's servers are a lot and I bet they use dynamic port ranges locally, making the issue harder to tackle.

TeamViewer has an option to set a proxy, but it doesn't use the socks proxy. I assume it must use an HTTP proxy, but in my end I'm behind a very restrictive proxy server (with authentication) which doesn't let me connect to TeamViewer's servers, and it's also the reason why I had to use socat (since it allowed to provide credentials).

Anyways, anyone have any idea on what can I use, either socat or another solution (I have cygwin, if it helps) to help me use the TeamViewer client? I tried logging on the web system but when I try to connect it launches the desktop client, so it's a no-go 🙁

Any ideas are welcome. Thanks in advance :)!