I wouldn’t worry too much about that. Plastic already degrades to a point of not being useful - it just sticks around in a way that is harmful.
Sunlight does a number on it, and it’s not very abrasion resistant. It’s also not great at weight bearing. We’ll be ok, and if anything, better off if something breaks down plastic (as long as the byproduct excreted isn’t just as bad or worse).
I’m pretty sure it’s just called a bird’s beak paring knife.
Reading further about it, it’s intended for tasks while holding the object you are cutting, rather than using a cutting board. Like peeling an apple in your hand.