It's perfectly okay to piece your borders. The quilt police are not going to get you. I NEVER cut my borders first as so many patterns suggest as sometimes your blocks may be a slightly different size and then you need just a sliver or two to make it the right size. I would much prefer to add a large p9iece than a little sliver, but actually either one works so just don't stress about it. If you aren't entering it in a juried quilt show it doesn't matter.