Why loops? Some instruments are built to use loop-ends rather than ball-ends, for example the bouzouki hanging on my wall.

...make a lasso of the string, rather than try to unwind it... I've tried that, but I've never managed to make a success of it. I came across this String Winders for Portuguese guitarras. I've never come across anything like that in any music shop. But it looks like a handy kind of gadget.   

Here is a YouTube of someone removing the ball and keeping the loop intact - so it can be done. But I've never managed to do it successfully. Fiddly work, but maybe with a bit of perseverance and practice...