He was at or above 37 % in each of the last three years before the injury bug knocked him out this year. I don't know what counts as significant attempts to you, but last season he took 156 of them is which more than 2 per game. In any other era that would have made him a marksman.
And it does beg the question... if a player does not shoot enough 3's to count as a wing under your criteria nor are they enough of a defensive anchor to be called a big, what are they? In Sabonis' case he is a 3 x All-Star and 2 x All-NBA so clearly he is something.