The Halacha only prohibits moving Mukse with one's hands. However, it is permitted to move any type of Mukse item with other parts of the body, including feet, head, mouth etc. This leniency is known as "Tiltul B'Gufo" and applies to all categories of Mukse. Accordingly, if there is a hundred-dollar bill on the floor, it is permitted to kick it to the corner of the room for safekeeping until after Shabbat. The Shulhan Aruch, in Siman 311, permits using one's body, even when the purpose of moving the Mukse item is for the benefit or protection of the item itself.
The Poskim discuss whether moving Mukse with the back of one's hand is also considered using the body, or is it deemed the regular prohibited use of the hands. The Halacha Shelema cites Hacham Bension (Ohr Lesion II) that it's permissible. Nevertheless, he marshals many sources, including from the Rishonim, that the back of the hand is prohibited just like the hand. Therefore, one should be strict and not use the back of the hand to move Mukse.
Another question on this matter is whether Mukse items that are normally handled with other body parts, besides the hands, can also be included in the leniency of "Tiltul B'Gufo." For example, is it permitted to kick a Mukse soccer ball? Hacham Ovadia clearly rules that it is prohibited. The leniency only applies when it is not the regular way to handle the Mukse.
It is permitted to move any category of Mukse item, with another part of his body besides his hands, even for the purpose of protecting the Mukse item. The back of the hand is prohibited just like the hands. If the normal way to move the item is with his body, then it is prohibited.