Composers like Joshua Billings and Jeremiah Ingalls pioneered the shape-note sound. Your best hope for finding instrumental music orchestrated in shape-note style would be to find names of composers from shape-note collections, then research those composers to see if they also wrote instrumental music.

You can sometimes come across instrumental versions of shape-note songs--Boston Camerata (besides singing many) has recorded a few instrumental-only renditions. I know that Aaron Copeland has done instrumental settings of some quaker songs; I'd be surprised if he hadn't set some shape-note songs as well. To what degree they'd retain the quality of the original harmonic treatments, however...