Thanks for the responses everyone! I ended up getting a long HDMI cable and using it with a usb-c hub I already had. The setup is pretty bulky so I might end up velcroing it per morgan's comment to reduce the pressure on the connection. And having a cable run across the whole room is... less than ideal. I think if I end up using this a lot, I'd probably just opt for a Steam Controller

If it’s about the touch pad controls you may want to check eBay for a Steam Controller.

I had mine in a drawer for years until the steam deck came out. Now I’m using it again quite a bit to play mouse-controlled games on my Steam Deck connected to the TV.

Not what you're asking for, but another option is to use a DualShock 4 controller which also supports touchpad (which can be divided in left/right if you want). I've found a pretty decent amount of community support and often use the touchpad (or gyro) for mouse games, though it's not quite as comfortable as the Steam Deck .

(I'm sure Dualsense 5 works just as well but I can only speak to Dualshock 4, which you can find for the cost of a HDMI cable online).

Genki makes the Covert Dock, which I have experience with. It's a bit expensive, but it's easily portable and works with both the Deck and the Switch. With a long enough cable you could sit a distance away from the TV and still use the Deck like a controller.

There are some Anker USB hubs with HDMI that would work for this application as well (in theory).

Cheapest is just to buy a dock/usb-c to HDMI and use a long cable (either long usb-c or long HDMI) to plug into your tv.

There are wireless HDMI dongles and even USB type c ones that would let this happen wirelessly, but you'll want to check reviews and make sure the latency isn't that bad.

Alternative cheap option is to get an android based tv stream box/stick, install the steam link software, and try to stream to that.

Finally you could just get a wireless mouse or some other wireless control option for using a computer mouse wirelessly. Keyboard with a laptop touchpad, trackball mouse, etc.

I hope Valve will release at some point a Steam Controller 2 that has the exact same buttons, trackpads, etc. like the deck.