This is part of the Smith listing in the 1908 Sears catalog, which states the damascus barrels were "bored for nitro powder" and had been proof tested
The standard 10g load then was 3 1/2 drams powder with 1 1/4 oz. shot in a 2 7/8" case; although loads with more powder, not shot, were available.
The barrels should of course be evaluated by a specialist with the interest, equipment (bore scope and wall thickness gauge) and expertise to properly do so. Assuming adequate wall thickness and barrels free of defects, and giving some reasonable allowance for the now almost 115 year old stock wood (and assuming the head of the stock is free of cracks), it is easy to load smokeless powder shells at pressures equal or even lower than those for which the gun was designed.
Pete Lister has posted a wonderful resource for loading the "Short 10" on the PGCA Forumhttp://parkerguns.org/forums/showthread.php?t=11403
Have you looked over the FAQs on the LCSCA site?https://lcsca.clubexpress.com/content.aspx?page_id=274&club_id=43784