Chords for "Glow Worm" (Mills Bros.)

The chords given for Glow Worm seem very bad. I'm assuming the melody starts with the notes: F# E E D# E. The first given chord is A, which has the notes A, C# & E, so the only match between the notes of the chord and the notes of the melody in the first measure are the E's on beats 2 and 4. My simple ear and brain prefers matches on the first and maybe the third beats. This same problem of mismatch between the chords and the melody occurs throughout the given arrangement. Maybe this is ok as some kind of jazz interpretation, but it sounds very dissonant to me. Is there a selection of chords for this song that would be easier on my ear?