I was shopping for a simple compact device which simply combines two stereo inputs into one, but couldn't find such a thing. There are a bunch of products with fancy mixing and such, but I am not interested in those. Long-life battery operation was another thing I was looking for. My solution turned out to be making my own.
This is just a couple of text-book inverting amplifiers with AC coupling on both inputs and output sides to minimize DC current draw from the battery. This way, DC current draw from the battery consists of just the opamps and the voltage divider for common mode generation. Total DC current draw should not exceed 21 uA. Optimistic battery life expectation is 220 mAh (from CR2032) / 21 uA = 416 days which of course depends on the actual usage of the device.
The PCB can be ordered at https://oshpark.com/shared_projects/KPojBfKX (I do not make any money).