You can do this other way around:

1. see what exception WebDriver is throwing in case if incorrect timeout type is given
2. wrap code, that sets timeout to WebDriver in try/catch block with that exception
3. when caught, then generate your exception with `$previous` parameter set to caught exception

This way you've be triggering Mink's exception on driver error, but condition used to determine error fact would be in single place - WebDriver code.