Unless this is a different issue altogether, the skipping is caused by the sound effects, even though it affects the music. If you have sound effects disabled, but leave music enabled, you shouldn't have problems.
However: Note that you must actually disable them in Lemmini. Just turning the volume down to zero is obviously not going to do the trick. =P
I've seen the issue occur in other Java games too, so it might be a Java issue rather than anything Lemmini-specific, or more so, to do with Java and specific formats of sound, with Lemmini using one it doesn't like so much.