It'll taste milder with the White so if you don't want that I would adjust it all by a third. The other way would be to mix the White with molasses to make your own brown sugar. Obviously assuming you have molasses!
I have a fudge recipe which calls for white sugar. It comes out really creamy and soft. I only had brown sugar once so made it with that instead and it came out a more crumbly texture. Still awesome fudge, but a slightly different texture. Interesting!