squffle

When you grab-hug and cuddle-rub a person or animal in an endearing but dominating way, leaving any hair or feathers in a right old mess.

A cross between "squeze" and "ruffle"

Variations:
squffles
squffleing
squffled

"Look at that squirrel! I would love to squffle him up"

"Your dog is being naughty again, must be time to squffle him up" *squffles him up*