I had the same problem, but I found a site that makes it fairly easy: https://onlineradiobox.com. I'm able to get to most of the URLs I want.
Search for your station.
Click on the station name.
On the resulting page, right-click on the orange "play" button, and select "Inspect (Q)"
This brings up the code containing the station URL.
Right-click, select "Copy" and "Outer HTML"
Paste that into a text editor, and select/copy just the URL.
(These instructions work in Firefox)