Not exactly what you're looking for, but looks like the MD4s supports a footswitch. From what I can tell in the manual, you can use the footswitch to do the following:
Stop --press footswitch--> Play
Play --press footswitch--> Play Pause
Play Pause --press footswitch--> Play
I don't have an MD4s - I've got a similay unit from Sony, but it has very similar functionality for the footswitch.
It also has an additional repeat mode which will play the given song one time through and then locate back to the beginning of the song - sounds like that's the sort of thing you're after.
It sure seems like there would be some sort of "play next track once and stop" feature, but I guess that's not how you're supposed to use the unit.
A super-low-tech solution would be to record your different songs onto individual MDs and then swap them out during the performance - obviously would require some manual dexterity to accomplish, and certainly not a good solution.