WT2003S mp3 greeting card
So I took a look at the WT2003S datasheet, and there is a command to change if the music should loop or not:

Unfortunately, it looks like this doesn't persist between restarts of the device. As you can see above, they suggest using an external MCU to run the play mode command every time your circuit powers on, which would work but is probably too complex for what you want to do here.
Interestingly, the datasheet seems to suggest that &quot;single play, no loop playback&quot; is the default. This makes me wonder if they got a customized version of the chip, which the datasheet suggests is possible? That would probably mean you could swap the WT2003S with a new, factory default one...but at that point I suppose you could just get a new playback circuit anyways.
Apart from that, the only other options I can think of would be to add a long duration of silence at the end of the MP3 track, or, like mentioned in the comments, to use a timer circuit to close the switch after a certain amount of time has passed.