Wave files are generally always, always much, much bigger than their MIDI counterpart, so that's nothing to worry about.
Looking at the wave file, I notice that, like I thought, there is a small delay at the beginning before the sound begins (about .15 seconds). Looking at the MIDI file as well, I noticed that there are two notes starting at the same time within it. If this is because you wanted it to be louder, you could just increase the volume of the note (which I've done) I've attached fixed versions of both files directly to this post. I tested the game, and it seems to work just fine.
I also trimmed the wav file so it takes up less space. I would have saved it compressed, but that begins to add a hiss if I save it as 8-bit PCM. I did also include an MP3 version of the file (compressed), but a problem with MP3 is that it inherently has a delay at the beginning that you can't get rid of (only .02 seconds though, much better). Take whichever one you want (my suggestion would be to go with the MIDI file frankly).
If there is still a delay when you play the game, the problem may be with your computer or sound card or version of DirectX.