Sousaphone is an instrument that's meant to be worn, so I would start there.

Maracas, some bells, and probably finger cymbals.

You could probably get a triangle or tambourine going, but it would be a bit awkward - especially the triangle.

Most breath-based instruments are out, due to the high speed, but you might be able to do interesting things with a Kazoo, or if you have real talent, a Harmonica.

So long as you were at a jog instead of a run, you could probably fashion an extra-sturdy harness for a small xylophone set and play it.

Edit for an afterthought: You might be able to get into certain string instruments as well. I'd start with something like a ukulele due to the small size and occasional low cost.

Marching drums are usually worn, although it's hard to run with tenors/snares.

Bugles