I believe that "I raise my hat" should be accepted. If not, how would you say that?
No, raise would not be a proper translation here. To say raise, you would say Je lève mon chapeau.
Considering enlever means to cause to be lifted, literally, like to elevate, it actually means exactly to raise one's hat. Just that it also means to lift off. Which one does, with ones hat, when one raises it to salute someone (which I assumed was the meaning of the sentence, which I now see is only one possible interpretation).
Consider the other meanings of enlever, though, all of which basically involve lifting things! :o)
In BR portuguese, to take your hat off to someone means you pay a lot of respect for this person and/or what he did. Is it the same case in french?
Oui ,en France les hommes se découvrent (enlèvent leur chapeau) par respect ou courtoisie .