The great thing about using electrolysis to remove rust is that it doesn't remove the patina. i believe the way it works is..
Rust is Iron Oxide. Electrolysis separates the Oxide from the Iron. it will not harm any good metal in any way.
There are many good write-ups on the internet about how to do it. just do a search for Rust Removal using Electrolysis.
For safety reasons i will says this.

Do not use Stainless Steel Anodes. There is Chromium in stainless steel which will create Chromates in the solution and this will be very poisonous.

Do not us anything for the solution other than Sodium BiCarbonate(baking Soda) or Sodium Carbonite (Washing Soda)
I couldn't find Washing Soda but OxyClean is almost the same thing and work great.
I have read about other people using other stuff but upon research found that it was unsafe.Using Sodium Chloride (Table Salt)creates chlorine gas which is unsafe.

Do not do this indoors. This process creates hydrogen gas, which is harmless unless it condenses and ignites.
Remember the Hindenburg?