Goddamn this thread is full of fail.
Chem PhD and ex-professor here.
You do not need multiple electrolytes. DC power source, positive to the ammo, negative to whatever the counter electrode is, as long as it conducts, it is fine. Like a nail or piece of pipe. whatever. The only safety concern is the resistance heating of the ammo. This could be an issue as if you want to remove the metals from the tip, you need decent currents. So you would not want to connect the positive to the primer or base of the case, which is more difficult anyway because it is painted. So just alligator clip to the projectile right before the case. You only want the tip submerged to dissolve it anyway. Copper is a better conductor than the steel case, the area being heated is mostly the bullet, which luckily is partly submerged in a heatsink (water) so the chance of the propellant or primer heating enough for ignition is low. (all the same, first time turn on remotely and wait, as well as using a low-current power source). Current can also be controlled by electrode spacing, the closer bullet and other electrode are together, the lower the resistance of the solution, and the higher the current.
In terms of electrolyte, your counter electrode will be producing hydroxide ions which will precipitate copper or iron ions from solution, potentially passivising the bullet and ending the process. You will want something acidic like diluted HCl (muriatic acid from the hardware store) to avoid this.
Now, as the process continues, stuff gets complicated. The bullet is a non-symmetrical electrode, so current densities are higher at points and edges. The very tip will be dissolved first, and you will see blue coming off of it from copper ions in solution. Once the copper is through, the iron core of the surplus ammo is shown. Iron likes to lose electrons more than copper so once the copper is breached the iron core will be removed leaving a copper shell. When all iron in range of electrolyte is consumed, copper will be dissolved off again. It will stop itself once the electrolyte is no longer in contact with the ammo.
Of course, set it up, turn it on remotely for a couple hours, and come back later. The chance of heating it up to ignition temp is low but high enough to warrant a couple precautions.
actually, the heat will be focused on the point of highest resistance, i.e. the thin steel case with laquer over it due to ohms law (I^2xR)