well now that i have my ball winder i don't think i would want be without it and i hate regular skeins of yarn because trying to find the beginning almost always requires me to rewind it into a ball anyway since so much stuff comes out of the middle when i pull.
that being said, i went for several months without one and didn't have too much of a problem. what i would say is carefully untwist it and pull it out into the big loop (kinda like the loop you start with when you start a game of cat's cradle ya know?) then i would grab one of those four boys of yours and have them get comfy and hold out their hands and start unwinding. if you can't catch one of them before they all escape the room then i would say wrap it around the back of a chair, i wrapped mine around my laptop monitor so i could talk to y'all while winding. there are lots of ways to do it.
and yes, i did start with the jumbled mess a few times. i can't help but find unknotting to be oddly therapeutic sometimes though.
goood luck! it can be undone, just be patient....and prolly wanna do it after those boys are in bed (assuming that they aren't 20 or hamsters of course)