As far as I'm aware for BDSM purposes you want to get the melting point low enough to not burn the skin, but high enough for the recipient to have intense sensations.
Paraffin and soy wax are common choices because their melting points (46 - 68 °C / 115 - 154 °F) are already lower than that of other kinds of wax.
Skin irritation
Stearic acid is used in many cosmetics, so the risk is very low.
The Safety Data Sheet of Vybar contains no indication that it can irritate the skin (apart from the obvious risk of burns). If you're interested in other additives, explicitely search for the Safety Data Sheet.
Both substances are mainly used to increase how much fragrant oil the wax can retein. It's those essential oils that often irritate the skin, not the additive itself.
Corrosion
I've seen several sites that claim that Stearin / stearic acid does corrode "flexible molds" (source). However, the term "flexible molds" means silicone, rubber, plastic and latex. It's true that latex moulds are vulnerable to stearic acid (source), but they won't dissolve over night. The corrosion would take several casts and progress slowly.
Some people probably misunderstood that or remembered incorrectly and started claiming that stearin corrodes silicone molds as well. But silicone for mold making is rather resistant to most chemicals, including acids. This site claims that stearin corrodes metal molds (which makes sense to me from a chemical perspective) and advises to use silicone molds instead.
Coloration
Both stearin and Vybar increase the opacity of the candle (you need to add less color to reach the same saturation). But they create different looks in candles: while Vybar reduces mottling, stearin increases it (source).
I honestly don't have practical experience with these and cannot help you any more. Hopefully a user with practical experience will share those with you.
Melting point
This is where it gets complicated and contradictory.
Pure paraffin wax melts at about 46 - 68 °C / 115 - 154 °F.
Pure stearin melts at 60 - 70 °C / 140 - 158 °F. This site claims that adding stearin to paraffin candles rises the melting point even to 80°C / 176°F. It also makes the candles burn slower and drip less (something you may not want).
There are 2 types of Vybar: Vybar 103 intended for hard wax and Vybar 260 intended for container candles and softer wax (like paraffin). Both increase the melting point of the wax (source), but I couldn't find any objective numbers. I assume that Vybar 103 increases the melting point more than the 260, but I have no proof.
Summary
Both additives mainly increase the amount of fragrant oil the candle wax can retain, but they also increase the melting point and seem to make the wax harder and drip less. Certain fragrant oils can irritate the skin and cause allergic contact dermatitis. I would probably forego the additive and light additional scented candles instead of scenting the "active" dripping candles too much.
