WWI hat cord identification help?

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I have my grandfathers WWI hat cord and need some expert advice.
1. I would like to determine what specialty or rank this cord represents?
2. What model of campaign hat would be appropriate for a late war display of this item?
3. Are there reproductions of the correct hat avaliable?
I know little concerning his service (primary and secondary sources long past) other than he was stationed for some time at Fort Pike
Little Rock Ar. USA sometime late war.
Attachment 34519
Other than his Remington Model 11 this is my only connection to him and I would like to document and display for the next generation.

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