Just use plastic, it's better for the environment anyway.
It will eventually biodegrade, but it's going to take a long time.
If you are worried about straws getting stuck in animals, a wax covered one will also get stuck.
The entire straw ban is the height of stupidity. Just start a "don't litter, throw it away" campaign and you'll solve 95% of the problem, without creating new ones.
If people actually cared (as opposed to wanting to look like the care) they would help start sanitation services (trash collection, and proper landfills) in Asia.
Maybe wax-coated paper, or a thin foil coating on paper, or some other kind of plant matter pounded into the right shape, or something.
Wax is a hydrocarbon that I believe comes from oil. I don't know how it breaks down on the environment but it's not immediately clear it's actually "better" than plastic, other than maybe not being seen once it falls apart.