So many great ideas posted!
To avoid recutting, you could stitch the squares, just as they are, into long strips, then join the strips with narrow sashing, either length wise or side-to-side. A border, then pieced strips all around and a final border.
The same method could be used to make two quilts by varying the colors of the sashing and/or having the strips run horizontally or vertically.
No trimming needed.