I do support that SHH directly or indirectly improves wound healing and other repair. We are working on an effect of SHH on injured peripheral nerve regeneration. You can search also pubmed, there is some literature available indirectly supporting this. I myself studied effect of SHH on Gli1 induction in nerve fibroblast and moving to in vivo system in mice and in transgenic mice:
Other papers are available as below:
Sonic hedgehog improves delayed wound healing via enhancing cutaneous nitric oxide function in diabetes.
Luo JD, Hu TP, Wang L, Chen MS, Liu SM, Chen AF.
Am J Physiol Endocrinol Metab. 2009 Aug;297(2):E525-31. doi: 10.1152/ajpendo.00308.2009. Epub 2009 Jun 16.
PMID: 19531636
Cutaneous wound healing: recruiting developmental pathways for regeneration.
Bielefeld KA, Amini-Nik S, Alman BA.
Cell Mol Life Sci. 2013 Jun;70(12):2059-81. doi: 10.1007/s00018-012-1152-9. Epub 2012 Oct 4. Review.