There are 3 different types of chainrings (someone correct me if I'm wrong though as I'm not that well versed in single speed/track tech):

track (designed for 1/8" track chains)
flat, single/multiple speed (3/32" chain)
ramped/pinned multiple speed (3/32" chain)

Given the measurement you provided earlier, you are not currently using a track chainring so that's out of the equation. That leaves you with the last two options either of which will work for your intended application. Because you won't be shifting up front, there is no need for a ramped/pinned chainring so any chainring described as single speed or just "flat" will work for your application.