The USB Logger requires a computer running weather software to make sense of the data and where to then upload it. The USB Logger does not offer these capabilities by itself and a router does not run weather software.
Getting a different logger like the IP Logger or the newer WeatherLink Live will allow you to upload weather data without a computer running weather software. But these aren’t your only choices. No computer required. But you’ll then be limited to only uploading data to WU and Weatherlink.com and the places that Weatherlink.com supports (like CWOP). I do also recommend the WeatherLink Live instead of the IP Logger.
If you’d like to continue to use the USB Logger without a traditional computer you could get a Raspberry Pi. These are tiny devices that are very affordable and use little to no power and can work headless without a monitor and without keyboad or mouse. The Raspberry Pi then runs Weather-Display or any other software you’d like.
Another alternative to keep using the USB Logger is to get a Meteobridge which you then plug into its USB port. This is a converted small footprint router that runs the Meteobridge weather software. You can still run Weather-Display on a computer if you’d like as it can get data from the Meteobridge. But I understand you are looking to move away from using a computer.
Another option is the WiFiLogger or Meteobridge Nano which both fit inside the Davis consoles. These upload via WiFi and are fully featured. The Meteobridge Nano is a bit more expensive but it is more capable. Some say the Meteobridge Nano is more complicated than a WiFiLogger but I disagree. Being more capable does not mean more complicated, you can just ignore the extra options and menus, because for basic use the Meteobridge is well designed and easy to use.