I don't see why the lack of power should prevent instrumental music at all. Can't you find someone who plays the fiddle, or pipes, or flute, or (well why not?) even accordion? Or some combination of these? I think a tune (with no words) would be better for a processional march, leaving the song idea until later in the ceremony. That gives you a lot more scope, as all sorts of tunes are powerful and stirring enough to serve the purpose, regardless of their titles. A single piper would provide a dramatic start to the occasion.

At our daughter's wedding, her cousin and uncle sang "One hand, one heart" from West Side Story, with guitar accompaniment. I think it's one of the simplest, loveliest wedding songs there is. But maybe not suitable for a march, better for a more reflective moment later in the proceedings.

Marje