Eezox is a sporting goods/gun care product. It does contain a minute amount of trichlorethylene and one should be familiar with its safe use. I will use uldn't use a lot of it in a small enclosed space and generally ventilate a bit if using it but its listed as quite safe in normal working conditions.
Typically I clean rusty strings using automotive chrome polish/rust remover on rags. This works better than steel wool and leaves no tiny bits of steel dust. Then I apply a tiny mist of Eezox with spray on a rag and wipe the string down with one pass in each direction to ensure its fully but extremely lightly coated. The use of this product requires a very light coating of it, when the carrier dries within an hour, the part should be dry to the touch...if not you are using too much.
I had similar product (high grade lubricant) tested, and nice to you if is stop rust, and but I am surprized, cleaning rusted strings is not possible only half of the string surface is cleaned and forget the section under bass strings.
Above some point it is better to leave rust, as the tone is worse when just a portion of the wire have been cleaned.. If for thé aspect indeed anything will do, I use 3M scotch Brite or an ink eraser.. Sure oils or WD 40 are attracting dust, and that damp the tone.
The marketing of your product is not very convincing, but if the product works....
Old wire and steel is often less sensible to corrosion than the steel of today. I it is easily seen on old tools.
Link to product>>>http://www.eezox.com/gun-care.html