Ian, for whatever this information might be worth to you....
Wood burning Shays typically used the classic "balloon" stack, also called a Caldron stack, or a "diamond" stack. The diamond stacks were frequently fitted with spark arrestor screens. Wood burners were usually found in and around logging operations because they could use mill waste for fuel.
Coal burning Shays, which were far less common than the wood burners, also used the Caldron or diamond stacks.
Oil burning Shays, which were by far the most common configuration, used the short, straight ("shotgun") stack like the one in your photo.
That much having been said....
On my own 2-truck Shay, I have the tall diamond stack mounted but a fuel oil bunker on the tender.

I "justify" it by claiming that the lokie was converted from a wood burner to an oil burner (which actually was not uncommon), but the stack never got changed. The "next time" the loco goes into the shop for maintenance, the crew will change out the stack.
