yes, such a cable would be very easy. You would just get a male and female 3.5.mm plug and jack, then just run two wires between them, and jumper the L and R channels.
Are you sure your player doesn't have an option for mono? For example, on an iOS device you can use the accessibility settings to change the sound to mono.
Would this not short a balanced connection? I think single-ended would be fine as they already have a common ground, which the OP appears to have from the TRS tip in the picture.
I assumed SE.