Even from when I was a kid, I always thought psyduck was not a duck per se, but rather a duck billed platypus.
Headcanon: Sidon, like any good shark, has electroreceptors along his brow/crest, something sharks may use to communicate with. Link, being not-a-shark, does not have these. But when Link is upset, and Sidon isn't sure how to help, he'll rub his face all over Link, sharing his electromagnetic field through touch! It doesn't really communicate anything, but Sidon acting like a huge cat usually cheers Link up anyway~