You could try playing to ALSA directly, in case the almighty PulseAudio is the culprit (the software daemon that allows multiple streams to be played at once) - ALSA is the default sound system on Puppy Linux.
A quick test case:
1.. Close any open audio programs.
2.. Stop the daemon from respawning:
sudo nano /etc/pulse/client.conf
Uncomment the line that reads:
; autospawn = yes
to say:
autospawn = no
Then press CTRL+X to save these changes.
3.. Stop the existing PulseAudio daemon from running:
pulseaudio --kill
4.. Now try playing an audio file from a media player of your choice. This will play directly to the hardware, but will mean only one program can play sound at a time.
To revert: Comment the line again (with a ;), and type pulseaudio into the terminal to start the daemon again.
If this improves the choppy sound, then PulseAudio is the problem and we can suggest some possible fixes.