Hand Clap Studio has its own pattern sequencer called Rhythm Xpander. This pretty much has you covered, but once in a while you start off in Rhythm Xpander and later want to do more advanced editing in your host sequencer. To avoid having to redo the pattern, HCS has a MIDI Export feature.
Just drag the pattern from the MIDI Export placeholder to your DAW. The correct claps and their velocities will be included in the MIDI. Don’t forget to switch the Rhythm Xpander off to avoid double triggering.