Random songs, looping on DFPlayer mini without microcontroller?

I've been playing with a DFPlayer mini in order to build a small, single function MP3 player for an elderly relative with Alzheimer's who has problems with much more than just turning on the device.

Originally, I setup an arduino to use the serial interface to just send the command to start random play, but it occurs to me that with all the capabilities built into the player itself, it may be possible to just have it play by itself.  I see there's a pin to short through a resistor to start looping play, but I assume this will play all the MP3s in the same order every time.  

Is there a way to randomize this?  My goal is literally a box with a power switch and a volume control (Which I am currently using an encoder to the arduino to send volume commands, but in the “player only" model, I'd just use a potentiometer on the speaker for basic volume control, at least to see how that works.

Is there a way to make an automatic play that would be random, without using a microcontroller?

Thanks in advance.. These players are awesome little tools!!

-Steve