You only really have 3 (4) options here:
1. What you mentioned, a 16:9 monitor - that isnt something you see viable so ignore that
2. Play the game in window mode in a 16:9 resolution / set YOUR monitor to a 16:9 resolution - this will have black bars on YOUR end though
3. Set OBS to a 16:9 resolution and fill the side with something like chat or some images or whatever - i'd say that is the most commonly used option, often seen with 4:3 games
(4). uncheck maintain aspect ratio and never get any viewers because it looks aweful since its stretched
One thing to note: You can NOT get rid of black bars in todays age, people have 16:9, 16:10, 5:4, 4:3 and what else as aspect ratios - someone WILL ALWAYS see black bars no matter what you do. 16:9 would be the most common aspect ratio though.
So i would either ignore it or go with the chat/images option since im sure you dont want black bars on YOUR screen while playing either. Thats about all you can do.
edit: what i wrote is about fullscreening the player, twitchs player without that is always forced to 16:9