The "oxalate crystals" mentioned above are usually removed in culinary use by peeling the yams then soaking in an acidic-based solution (usually diluted vinegar).
Otherwise, well, that's a lot of oxalate crystals that may cause itching. The itching here is generally caused by physical instead of biochemical processes, basically having multiple tiny crystalline needles raking across your skin, especially when you're peeling the yams bare-handed (though improperly prepared slimy yam paste can itch the lips and mouth too).
But some people are also allergic to the yam (proteins), so in their cases the itching is also "biochemical".
Edit: Huh... looks like I mentioned it before in another post from some time ago.
(...) Yamaimo is generally nontoxic even when raw, but they contain tiny, needle-like crystals of sodium oxalate (concentrated near the skin). On contact, the crystals basically inflict multiple tiny puncture 'wounds' on your skin, which itches like hell. This isn't an allergic reaction though, strictly speaking. More like triggering the nerves responsible for sensing pain on a smaller scale (causing itching instead of pain) but over a large area (that's why it itches A LOT).
Yamaimo is generally eaten raw, grated into a gooey paste. Proper preparation of yamaimo (as hinted by Demundo) first involves peeling it thickly (to remove most of the aforementioned oxalate crystals) and then soaking it in diluted vinegar or some other acidic solution to dissolve the remaining oxalates. Now it can be grated and used for food.
(Also, when grated, the starchy, gooey matrix also helps to bind and shield any remaining oxalate crystals, so some people can just get away by wearing gloves and not bothering with the soaking process.)
Of course, some people are also allergic to yamaimo proteins, so they itch even more when handling or eating it (dangerously so, sometimes, depending on severity of the allergic reaction).
TL;DR: This is real-life itchy "slime". Comes up every now and then in Japanese comics as a semi-comedic instrument of "torture" (like that Kancolle example). Though here von Trapp is probably testing out a new "trap material" (likely for an Itchy Slime trap, or a further improvement to the Clothes-Dissolving Slime trap on the previous page) that his poor harangued Assistant is obliged to help with.
Adding some relevant medical knowledge here: oxalate crystals, as you might have known, also contributes in forming 'hard' kidney stones that may persist even after several 'shots' of lithotripsy. Oxalate crystals also dissolve in warm water better than in cold water, so if you handled taro incorrectly you'd better wash those hands with warm water and vinegar, not soap.
Aside from that, few things that also helps dissolving oxalate crystals includes: citric acid, chloride, sodium chloride and calcium hydroxide...the last two being the easiest to get, since it's basically salt and prevalent in any kind of toothpaste!
Also, please don't get ANY kind of these itchy slime in contact with your mucous membrane. That also extends to use them as lube.
It itches...
Yamaimo (and nagaimo) both have oxalate crystals in their skin that can cause itching.What is this?