The canopy is of the same fabric as the pirate ship sails. And the ships are designed for being played with in water.
I would say it is definitely more cloth than paper.

They are pretty robust against water and stay in shape. I cleaned several of those (well, more sails and roman tents than canopys).
Still, I would not tumble it. So warm water with mild soap and flat dry would be my suggestion also.
best,
socrates