Skin-So-Soft is mineral oil with fragrance.
You can somewhat delay or hide the effects of aging of old vinyl with mineral oil, but you'll never replace the volatile organic compounds that have evaporated into the air over the past few decades.
If you want to save it the best you can in the condition it's currently in, the best way is not to use it at all, and seal it away in a plastic bag in a cool, dark place.