A problem with your bet is that the proposed idea of stripping electrons from atoms is quite disconnected from reality at several levels. Atoms need electrons by definition. Almost all of their physical properties and behaviours are due to the balance of the negatively charged electrons with the positively charged protons in the nucleus.
If you removed electrons from a small (say a gram) ball of iron, the electrical repulsion from the remaining protons would exert an outwards pressure at the surface of the ball which would measure in the thousands of millions of tons.
The electromagnetic force is enormously stronger than the gravitational force. You must remember that when you rub a balloon on your hair, pulling electrons from your hair onto the balloon, and sticking it to the ceiling with that electrical charge, that force between a (relatively) few charged atoms on the balloon, and the induced charge on the ceiling, is exceeding that of the attraction between the balloon and all of the atoms in the planet, which define the gravitational force downwards.
So good luck holding anything together when you remove the electrons. The forces uncovered (normally cloaked by the charge balance within the mass) are so large as to almost defy comprehension in an everyday sense.
The iron atom nuclei that make up your electron-stripped iron ball will just fly away, or try to very, very, very hard -- and no substance we could make would have a chance of preventing it. Of course, as the "electron-less iron" expanded it would take less and less pressure (both total and per surface area) to hold it in, so ultimately one would be able to contain it. But it would also be pulling at all electrons in the nearby vicinity with a fantastic tug enough to strip them off nearly anything -- so the simple thought experiment in the way you pose it could never happen in reality.
[Editor: Your point about the similarity in size between a hydrogen atom and a proton is perhaps beside the point. The electron cloud around iron is 26 times bigger than hydrogen. Because of this, the physical interactions of iron are much more various and complex than hydrogen which is the simplest of elements. In any case the same point about tremendous electromagnetic forces would apply even in the case of hydrogen.]
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