OK I took a look on GE. My guess is that it is the Laramie River but not sure. The run is below Wheatland Res #2 and flows into a small reservoir (which feeds Bluegrass). You can see one end of the diversion tunnel on the south shore of the small reservoir (41°55'22.87"N 105°25'32.52"W) scroll south about 1/2 mile or less and you'll see the other end of the tunnel pop out of the sage brush and into the beginning of the Bluegrass run (41°54'54.83"N 105°25'18.78"W).
There looks to be a good take-out here (41°56'5.08"N 105°31'7.42"W) but that would make the run just over 3 miles. Your proposed take-out is at the southeast shore of the small reservoir, making the run 9+ with intermittent rocks/possible rapids and a fair amount of flat water, interesting.
My guess is that the Wyoming BLM Rawlins field office would have more info about land ownership, access, and proper names.
Let us know what they say