I'm not sure "having his hat on askew" is correct. Since "askew" is an adjective [ after verb ] or an adverb, so I would said "having his hat askew" or like @abx said using "tilted", that would be "having his hat tilted".Just saw a little boy, more than one year, probably 2 years old, having his hat on askew, staggered about. His mom told him : you couldn't walk by yourself. There are too many people around. You should hold my hand. The boy said: I wasn't born yesterday.