Straw is a brown. Last summer when I ran out of fall leaves, I bought a bale of straw and used it for mulch and for brown in my compost. In my not real hot compost pile, the straw didn't break down as fast as the leaves do, but it did eventually break down.
I don't think that 96:4 ratio sounds right.
"Scientists (yes, there are compost scientists) have determined that the fastest way to produce fertile, sweet-smelling compost is to maintain a C:N ratio somewhere around 25 to 30 parts carbon to 1 part nitrogen, or 25-30:1"
But since that straw is 75:1 while even greens are usually in the range of
15:1 to 30:1 (yes, your high N sources are still 15 times as high in C).
That means if you make your pile 50:50 greens to browns by volume, you will come out with somewhere around the right ratio. How convenient!
So everyone can quit stressing about C:N ratios and just make sure their compost piles are balanced between greens and browns!