Viewing your pictures and description, my first observation is: Consider getting an independent opinion whether the standing rigging appearance is just cosmetic or the condition has deteriorated to an unsafe state. From what I have read, and also in conversation with several rigging companies in my area, depending on the boat's location (temp/humidity/FreshOrSalt water) and usual sailing wind conditions, standing rigging should be replaced every 7-10 years. ( I myself am right at 10 years so I will be re-rigging in the near future!) It's not only the SS wire, but the condition of the chainplates and all of the connecting fittings and bolts/nuts. The protection tape in your pictures also indicates it has been a while since the rigging was inspected and maintained.
But if you are willing to forego the safety aspect, the best product to brighten things up is SpotlessStainless. Use the forum's search function to learn more. It will restore rusted stainless steel with just brushing on, then rinsing off after several minutes. Looking the severity of your rust as shown in your photos, will probably take several applications for you. SpotlessStainless will also remove SS rust leach stains from the gelcoat.
My experience with a failed rigging part happened about 5 years ago. Although 1) the PO had re-rigged the boat just before I bought it, and 2) 5 years later I engaged a professional rigger to do a safety survey, my forestay broke loose in 25 kt winds one morning. The double-jaw toggle connecting the forestay to the stemplate at the hull failed. I was lucky that I didn't loose the entire rig. The foreward shrouds held and I was able to change quickly to a downwind course to relieve the backward pressure on the mast. Inspecting the part afterward (see photos), I realized that although the SS rigging had been replaced, the rigger re-used the original double-jaw toggle fitting. From the outside it looked fine to my surveyor. Underneath, stress cracks had already started. Several months later -- Bam!