Test both methods on a scrap piece of cloth to see which medium works the best.
Paint on a thumb or fingertip would generally leave just an oval shape, while stamp pad ink would leave a more defined fingerprint, in most cases. You just have to decide which look you want to go for.
But I don't see the point of offering the guest the choice of green. Unless you have a lot of guests, your tree is going to look pretty naked. Perhaps you should fill in all the green leaf shapes yourself, ahead of time, and then the guests would just be adding their color choices over the top of the leaves, like fruit.