In the old days, no one really cared about serial numbers. Only "quality" makers put them on, primarily to keep track of upgrades and as part of a warranty system. They could also be used as inventory control by stores or the larger users, like the military and police. There was no legal requirement to put them on and few gun or hardware stores bothered to record the numbers when they sold individual guns.
Also, by 1888, that Navy would have been an old piece of junk. Before about 1880, some people still liked to use cap and ball because the components were easy to get in remote areas, but by 1888 fixed ammo in common calibers was certainly available, even in Idaho.
Jim