I found this file... looks like anything goes...
NO! That diagram indicates that there are several "standards". And you must select the correct one, or you will surely toast your MP3 player gadget.
Do I just try to make a cable and see what happens?
NO! Unless you were going to throw away that gadget anyway.
any chance of frying the player if I have the power polarity reversed?
YES ABSOLUTELY! If you get this backwards, its all over, toss it in the bin.
Or the data pins flipped?
The device probably won't communicate with the data pins flipped, but it probably won't smoke it.
You could either trace out the wiring between the battery and the connector to determine the pinout, or else insert a TRRS plug into your gadget and probe it with a meter to see if you can find any residual battery voltage (to indicate power polarity).
IMHO, after you get the power connections right. You can try the data leads both ways and see which way works.