You probably have more control than you realize about the URL since you say you are using MyBinder. In fact the example on the jupyter-notebookparams page uses MyBinder.
If you study the example launch badge URL there (i.e., https://mybinder.org/v2/gh/manics/jupyter-notebookparams/master?urlpath=notebooks%2Fexample.ipynb%3Fa%3D1%26b%3D%22whatever%22%26autorun%3Dtrue) you’ll see there is no second question mark or quotes because the text is ‘escaped’ after the ?urlpath= portion.
If you go to here and then paste in the box on the left the end of the URL the launch badge uses notebooks%2Fexample.ipynb%3Fa%3D1%26b%3D%22whatever%22%26autorun%3Dtrue, and then finally press ‘Decode URL’ button, you’ll see that ‘escaped’ part decodes to notebooks/example.ipynb?a=1&b="whatever"&autorun=true. So for MyBinder use you should be constructing your URL similar to that badge as well. And you can use that same site to encode it for the link you’ll use to launch MyBInder with your notebook. You’ll use the ‘Encode URL’ button to convert that final portion that includes your notebook path and name and the variables you want to set, and place it after the ?urlpath= portion of your typical MyBinder URL.
For example, to pass different parameters, a = 42 and b = 'foobar' to the test notebook, you would construct the URL Binder as a URL. Go ahead and click on that link and you’ll see it launches via MyBinder with those settings now.