The Military predominately as matter of old habit used the rolled towel cone by far. There were a number of private market devises being sold for that purpose, which may or may not have seen actual military use. Some existed during the 1860's (ie: Chisolms, Morton, Snow) yet many out there were actually post-war. (ie: Clover, Hewitt, Hare) Im not aware of any mass purchases of such devises by the army.
Im not sure which metalic instrument your specificly referencing... But have frequently seen at various sutlers the handled copper funnel item with the small sponge retainer bracket/bridge inside... Which Ive seen many in the reenactment community blindly jump on... however I personally would be suspect of both of its period authenticity and preponderance of use... or lack thereof... If in doubt... stay with the towel... tons of documentation of its use...
Just an opinion and observation..
Lieut Frederick Sineath
14th Virginia Infantry Regt Co.I
- 106th Penna Vol Co.F