While I don't know much about strops, leather and I are old friends. Latigo is commonly oil tanned cowhide, and 'shell' horsehide is also known as cordovan (not the color, two spots on the horse's butt that have exceptionally fine grain and density)..
that horsehide is used for strops and the finest shoes and boots, and is worth owning when you get a chance at it.
The quality of latigo wouldn't likely approach that of shell horsehide, disregarding price. I'd get the horsehide and take everyones suggestion to finish on linen, strictly on grounds of quality and longevity.
As happens, I've a side of saddle leather I was wondering about, if 12oz oak tanned could be used for a strop..and it's heavy enough but I've no clue if it's suitable otherwise.