I once asked my relative to go in to a Kingdom Hall and get a copy of a Watchtower that was spewing it's usual venom against apostates. His cover story was that he should tell them that his invalid Aunt was a Witness and asked him to get a copy for her. I suggested that he go well dressed. He didn't, which may have contributed somewhat to the situation that ensued.
He got immediately challenged in the Kingdom Hall parking lot by a brother who was keeping guard duringthe meeting (Fear of car vandalism in a good neighborhood or perhaps of apostate literature being placed on the cars?). He managed to get in but was questioned at length before he managed to get a copy. He made mention of how paranoid they seemed. This was in the mid 1990s.
I don't know what they do with their 'secret' Watchtower magazine after the meetings-I suspect they collect them and throw them away. So if you were to want one showing up as a stranger you would likely arouse suspicion, even if you get away with impersonating a Witness.
Villabolo