Just do the binding, whichever way you feel comfortable doing it. IF anyone says anything negative about it, just tell them you prefer it that way! That said, there are tutorials, which show how to do painless corners. Just takes a bit of practice and before you know it, you have a nice, mitered corner!
BTW, if binding corners really, really upsets you, you can simply add a border, then round off those corners a bit (use as small saucer, ribbon spool, or whatever, as a pattern) and use bias-cut binding, around the whole thing. The curved edge will be fairly easy to finish neatly.
