I have been making a home-brew cleaning fluid for 25+ years that is comprised of a gallon of distilled water (less 1 pint to allow space for the next ingredient), 1 pint of 99% pure isopropyl alcohol (available in some drug stores), and a few drops of a liquid surfactant (I got some from a chemical supply house, but you could use 8-10 drops of liquid dish detergent in a pinch).
This solution cleans vinyl LP's very effectively, and it has never caused any damage to the more than 2000 LP's that have been cleaned.
As for stylus cleaners, there are two schools of thought on the subject. One school thinks it's OK to use liquids to clean the stylus, and the other school thinks it's a dubious idea. I am of the latter school, since liquids can wick up the cantilever by capillary action, and fluids do not enhance the linearity of the coil/magnet assembly. Hence, I prefer to use a dry cleaner, such as tip of a soft brush (like a small art brush with the bristles cut at a 45-degree angle), or the soft stylus cleaner "blob" that is currently on the market.
If you decide to try this semi-viscous quot;goo"/adhesive, let me suggest a way to save a lot of money: buy a jar of the product sold as "Clear Museum Gel" that is distributed by Trevco of San Marcos, CA. This "goo" sells for $10 for a 4-oz. jar (rather than the audiophile product that Audio Advisor sells for $69 for a 1-ounce amount), and from all I can tell it is the same material. It sure works the same way, based on my personal experience. I have seen the "Museum Gel" in stores that sell glass and ceramic collectibles, and in several local hardware stores (including the Lowe's chain), so you should able to find it without much trouble. A 4-oz. jar should last for years...