It's hatt in singular, with two ts, otherwise it means "hatred". :)
I think the problem here is really that English and Swedish use reflexive pronouns differently. If you translate it literally into English, it becomes "he takes the hat off himself" - so the definiteness is still there, much in the same way that it would be for e.g. jag ser hatten ("I see the hat")..
But where Swedish typically uses constructions such as tar av sig/dig/mig (etc.)., English uses "his/her/my/your" (etc.). So the quirk is really that translating to English changes the noun phrase to require possessive form.