You can make a lot of half-square triangles with those 4" squares. I'm thinking a star pattern. Like one in Quilters Cache:
http://www.quilterscache.com/P/PiecedStarBlock.html
Just use white fabric where the black fabric is. You can also find a pretty fabric to fussy cut for the center.
I always like to use 4" squares when making 3 1/2" half-square triangles. Some people like using 3 7/8" but I prefer 4" because then I just square it up afterwards. With 3 7/8" squares you have to be very careful with your seam allowance.
Please tell us what you decide.