Disclaimer: This question comes from a physics student.
I was studying electrostatics and I was wondering how to charge a conductor at home without any fancy furs etc. So an idea came to me: take a battery, touch for example the negative terminal with the conductor and then remove it. Since the negative battery terminal is at a negative potential and the conductor was previously grounded ($V = 0$) then as their potentials must become equal, it means that electrons will flow from the battery terminal to the conductor for a short period of time. Afterwards, I disconnect the conductor and the electrons remain 'trapped' in it hence the conductor is now negatively charged.
At least that was the idea. Now suppose that the battery is a galvanic cell ($Zn, Cu$). The question is whether there are free electrons floating inside the $Zn$ anode when it is not connected to the cathode?
The whole system (battery, wires) is electroneutral while the current is flowing e.g. Zinc atoms at anode dissolve and electrons stay at the anode while the $Zn^{2+}$ ions go to the solution, but in the same instant other electrons leave the anode.
When the electrodes are not connected, I'm not sure would the redox reactions happen. In my understanding, $Zn$ oxidizes because $Cu$ on the other side has greater electron affinity, but $Zn$ would have to be able to 'sense' $Cu$ on the other side somehow, otherwise the oxidation reaction happens anyways for a short time until it reaches some equilibrium point. This is what I think actually happens and that's why the anode would actually be negative until connected to the cathode.
So am I on the right track with this and ultimately, will my attempt to charge the conductor a bit succeed?