I think I see what you're getting at..........

The brim of the cap would be lower than my helmet visor. I could tilt it so that it would just brush the tops of the glasses, giving more shelter.

I have a summer helmet that I fastened the bill and sweat band from a baseball cap into. Maybe I could try to work out something similar in my winter helmet.

I'll give it some thought and, likely, experimentation. Thanks.