If you want them all to stay away from page borders you'll need to do that yourself. Pepakura Designer will work for that. You'll have to separate the pieces into small enough parts and move them around a bit. You can just print it out, realign the pages so the lines match up, and tape them together, though.
If you have a cutting mat with a grid it's pretty quick and easy to line pages back up, tape them together and then cut out the large parts. If you use cheap enough painters tape you can peel the stuff back up no problem and adjust if you bork it!