You can run Slackware without PulseAudio - using apulse. apulse is a hack - a wedge library that provides a fake PulseAudio sink that programs that only seem to want PulseAudio can use, that dumps the audio data directly to ALSA. There are a few caveats - apulse provides nothing but a sink, and duplicates none of the other functions PulseAudio has usurped, so things (such as the KDE volume control system tray item :( ) don't work as they should. It's ok, the command line alsamixer works fine still for volume control. I haven't found a program yet that really complains that much about it or at all.
Once you've slackbuilt it, uninstall the distro pulseaudio package before you install apulse. It's also best to drop to init 3 and kill the pulseaudio daemon before you uninstall it.
% killall pulseaudio
systemd/pulseaudio evangelists or sealions in the comments will be deleted.