I'm making my former comment an answer so that I can put pictures to explain better.
First, don't mess with the grips. If they work fine with your hands dry then they don't need anything. If they don't work with dry hands, then do something to them, because using gloves shouldn't help much in that case.
Then, going to the gloves subject. Even if you ride a bike and fall down at <10km/h you can scrape your palms really bad, so a scooter will be way worse. In my opinion you shouldn't even consider riding anything without a basic pair of gloves - because you can choose gloves with zero discomfort and extra sweating.
The palm of your hand is anyway always in contact with the handles, you can't count on that part to cool your hands, so it would be the same thing if you have it covered with something protective and with better grip. For the back there are synthetic materials with huge breathability that won't bring any discomfort, even if you're not moving fast. Get something that has this structure:
(I'm not endorsing that company. Any other brand will work the same, as long as it has a hard palm and a breathable mesh back.)
Of course, these give you just basic protection in case of a crash, but I think that they are the best compromise for a scooter in warm climates and that basic protection is way better than bare hands and you also get your grip problem fixed.