I would leave the papers in until each hexie is surrounded on each side.
I've done it both ways, leaving the basting in and taking it out. If it doesn't show and you don't have too much of a seam allowance (if it's not too bulky!) it's not bad to hand quilt, might take a bit more finger strength. Personally, I prefer to leave the basting stitches in.
And just remember - your quilt, your rules!