I would not recommend the electrolytic rust removal. It will remove some iron (etch the surface) as well as removing the rust and all the bluing. Notice how gray the plane in the tutorial looks? That iron that's been left with an activated dull matte surface. You'd have not only to get the water displaced and oil on it fast, before it rusts some more, but the surface will now be a different texture than previously.
A better approach, if you have a container large enough, is to put some low ion (soft or distilled) water in and bring it to a boil, then set the rusty part of the gun in for about 15 minutes. If the rust is fresh and light enough, this will convert it to black magnetite. This is the basic principle behind how rust bluing is done, though that process has a more controlled light rusty surface. Once converted, the black oxide is mostly looser, as well, and you and wipe it down with very fine steel wool or even with rough brown paper towel. Also, when you remove steel from boiling water the heat not only dries it fast, it causes a thin blue oxide layer to form that helps protect the metal long enough to oil it or get another finish on it.
If that boiling doesn't convert the rust (if it's too deep or has oil in it), another product I really like Gunzilla. It's a gun cleaner, but it very slowly does a top job of loosening rust. Just leave it on for a week and rub most of the rust off and repeat. It's slow going, but probably the most gentle approach. It won't remove the blue at all.
If you don't have time for that, PB Blaster or Kroil or other penetrating oil left overnight will loosen it and two or three treatments like that will probably get most of it. Not quite as gentle as the Gunzilla (which is also safer on your skin, being a biodegradable vegetable oil product), but won't hurt the bluing any, either.
Only at that point that the rust is largely gone and you can see how the metal looks underneath are you going to be able to assess the damage well enough to determine how much refinishing and what kind is really needed.
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