I understand (in the layman's sense) that properties of an individual element are mainly derived from characteristics of its outer shell electrons...e.g., why is zinc so different from copper when they differ by only one proton and electron. My question is this: (although it is physically impossible, I assume) could you swap one random particle (proton, electron, quark) from a random tungsten atom, say, with the same type of particle from a random antimony atom, with there being no difference whatsoever in either of the resulting atoms' properties and characteristics?
You are correct, the swap would make no difference as long as the swapped particles went into the same quantum states (electron shells) that were previously occupied. Furthermore, when theorists calculate the states of multi-electron atoms, they have to take into account that all the electrons could be interchanged within the atomic shells without affecting the result. This leads to an electron-electron interaction term called the exchange interaction that has to be included along with the regular electomagnetic interaction between electrons when doing the calculations. The exchange interaction is a completely quantum mechanical interaction that has no counterpoint in classical physics.