How can I go about ordering a replacement? Or are there 3rd party power cords that would work?
It depends on the model of TensorBook that you have. The newer ones are Razer Blade laptops, so they use the same 230W adapter as this example here: Amazon.com - There are lots of them on Amazon, so this is just one example. You can just search for “razer blade charger 230w”
Not sure about the older models