I love using Magic Eyes Sweet Lotion with my Handy.
Very slippery but not too thin for comfortable application. Takes at least 20-30min before it starts drying out and can be very easily readjusted after that by adding just a medium drop of water/spit.
It’s not super expensive at 15-20$ per 220ml bottle and seems to be pretty much globally accessible.
Unfortunately I have no idea about the ingredients, other than that it’s said to be water based.
ToysHeart Onatsuyu is also a fine, common choice and fairly cheap - but in combination with the Handy sleeve it’s a bit too thick for my personal taste.