You cannot skip cutscenes, however they patched in a speedup key in a later build, which is the one on GOG and Steam.

The speedup button is also usable during normal gameplay, so you can speedup overworld movement, battles, etc.

I've planed to route/run this game for a while now, but haven't really gotten the time and motivation yet.

(Also sorry for responding kind of late, I apparently didn't have notifications on for this game.)