Is there a way out? Perhaps: you can try to play the game in two opposite directions:
(1) declare that the nail was not part of your "real" body in the first place; that your real body is, well, closer to your head for instance. And stubbornly keep this view of "otherness" accepting all its consequences, which means that your body will shrink more and more until.. until what? until it reaches the little homonculus in your cartesian theatre? You have a better, more profound retreat though: to conclude that you DON'T have a body.
(2) take just the opposite strategy: what about saying that yes, the nail already cut is still your body? Well, this will produce an avalanche of reasoning that will make you conclude that the whole world is your body.
In both cases, we would be forced to conclude that the concept of "body" is an useless one (thanks Occam!).
But the concept of body is not useless at all! we communicate and refer to this concept all the time. This is because it is an useful convention, a functional definition of a part of the process of knowledge gathering (just like "living" animal, or sentient being, or self, or... - but I am going to quickly here). Let me add something before I take another angle of attack on the model of mind/body/world. There is, I believe one one way out yet it will take us in a completely different direction, by giving us a new insight: let's go back to the scissors that are cutting the paper. If you were obliged to declare that the scissors are part of your body, what reason would you (reluctantly) give? Perhaps that they act "as if they were part of your hand": which I read as: their FUNCTION enhances the function of your hand, the action of the scissors is not an obstacle to my intention of cutting the paper, but it just HELP "me" doing it better (it even redefines and clarifies the intention of "cutting" something). One can even wonder to which extend the "intentionality" is not a by-product of the availability of a function, of the capacity of acting on the world. From that point of view, the scissors, or the body for that matter would be defined inasmuch as it can create patterns of action, and enable (create!) intention. But given that the boundary between the "world" and the "body" is ill defined, we have to conclude that the world itself is a critical "part" of ourselves (the self defined as the subject/object capable of intentionality).
Now, before developing this view further, I will come back to the initial problem and take another angle of attack. Suppose that from the very first day of being born, I perform on a baby some little grafts: I add an additional arm, controlled by the muscles of the abdomen (as Stelark has done during his adulthood), then I put a permanent green pigment on his cornea, so the world would be ever-green, then I put ear-aids that act upon the surrounding sounds, so that, for instance, the individual would only hear a discrete, temperate scale of pitches instead of the continuous range of frequencies. Most would say that the so modified human being won't be experiencing the "real" world. That the perception of the real world has been modified by some sort of artificial prosthesis. But this statement does not resist analysis: if you were born blind, or deaf or without arms or skin sensation, then you wouldn't be experiencing the "real" world? This is at least politically incorrect: it would mean that the only one entitled to "experience the real world" are those born with sight, legs, arms, etc. We are forced to conclude that what some call the objective reality is no more than a convention - a democratic one though.
So, the body (defined as the conventional human machine) clearly modifies the nature of the experience we have of the world, but what I intended to show here is that the very idea that there is a world out there mediated by the body is wrong: the world, the things that we call "the world" are "experiential invariants" of the action-perception loop created by a certain form of the body (which as we have seen is an ill-defined concept, and variable, modifiable).
In other words (worlds!): the model of world/body/mind is misleading, it is like the shadows in the cavern. A poor description of what is really going on.