"……..the possibility that Hydrochloric Acid will react with Iron in the tap to make Iron (III) Chloride. Now that chemical is well known for dissolving copper to make printed circuits. "
Not quite, the reaction between HCl and Fe will produce ferrous (III) chloride irrespective of the acid concentration.
It is the ferric (II) chloride of course which is the etchant. However ferrous chloride does attack Cu to a lesser extent though with the problem described any effect would surely be insignificant.
If Andrew T does decide to use either alum or dilute HCl, it's important to keep agitating the solution with a piece of thin wire in order to displace the hydrogen bubbles which will form on the tap's surface and prevent the reaction. Also keep the reaction warm for a faster dissolution of the steel.
Forgot to add > if a thread lubricant was used before breakage then this will inhibit acid contact with the tap, so degrease as much as possible first with some solvent.
Edited By Fowlers Fury on 14/09/2017 16:21:24