treeing walkers were created simply by breeding running walker foxhounds that treed to each other until treeing became a consistant trait, so their conformation should fall within the parameters of the running walker, which brings me to the next point.
running walkers are american foxhounds, so are julys, goodmans, triggs, pennmarydels, croghans and many others i'm not familiar with. there is enough variation between the lines that they are defacto breeds. all three croghan blooded dogs i've seen had the blocky head of the english foxhound. it's also common among the julys. and since the lines are crossed and then bred back to the line the traits can popup among ANY line. further american foxhounds were developed from english & continental hounds so the traits of all the contributor breeds exist somewhere within the dogs.
most fox & coonhounds of value, for say competition hunting are tatooed or freeze branded. most fox & coonhounds used for running deer are not, nor are most meat/pleasure hunting coonhounds. also valued hounds are run w/ tracking collars to aid in recovery.
sooo unless you have the pedigree only serious foxhunters can tell a dogs bloodline just by looking.
if i HAD to guess i'd say croghan or english.