Ideally, you need a mic and a speaker inside each ear so sound can be localized by turning the head. You can put the electronics and battery in a separate box,

Ideally, you need a mic and a speaker inside each ear so sound can be localized by turning the head. You can put the electronics and battery in a separate box, but wired is better than bluetooth/smartphone because it's hard to get the latency small enough with BT and a smartphone. (This is tougher with Android than IOS.) You don't want the direct sound leading the processed sound in the ear by more than a very small time. Probably single-digit milliseconds, IIRC.