Of course you can do this! Just think - when I made my first quilt (also a Trip Around the World), I did it all by hand. I cut all the squares by drawing around a template and then cutting with scissors (rotary cutters hadn't been introduced yet). I pieced it by hand, starting with the center square and adding squares all around, and then put it on Grandma's quilting frame and quilted it by hand. So whenever you think you're running out of patience - think about how much more you'd need to be doing it the "old-fashioned" way!