This is kind of a weird question because, as you rightly note, open games usually are more tactical and sharper than closed games. But it is possible to play 1.e4, and by extension the open games, in a quieter and more positional manner than is usually done.
The most famous proponent of this way of playing is Anatoly Karpov, who played 1.e4 throughout his life and is nevertheless regarded as a very positional player.
But the player I would recommend you study is a different one:
I have always found that, of all world class players nowadays, Mickey Adams is the most instructive to follow. Like Karpov he is a 1.e4 player and something of a positional genius. Unlike Karpov he doesn't rely on a team of seconds to get him to the forefront of theory, so I have always found him to play more "ordinary" positions. If you look at his games you can usually easily imagine getting this kind of position in your own games (unlike some super sharp 30-move theory battle other players indulge in).
Generally regarding openings this would mean playing the Ruy Lopez against 1…e5, the Tarrasch against 1…e6 and either the Rossolimo or some short castles + a4 + f4 against the sicilian.
Against 1.e4 you would play e5. And against 1.d4 I think Adams usually plays the Nimzo, though that might be outside the scope of this question aka open positions.