They're usually pretty light winds, like a normal day. However, the eye has to move directly over you to get this effect (meaning you're going to get hammered by the eye wall twice). Otherwise, it's a hurricane all the way through for you.
I suspect that you could take your MP out and fly during the eye, but it would probably only look like a stormy day off in the distance in most directions. Probably not very "cool" - the same lack of "awesomeness" that people thought they were going to capture during the total eclipse. I guess you could survey the damage thus far without worrying about the FAA's TFR but it's only half over at that point any way.