Not really, no. The records of Company I of the 2nd Cavalry MSM tell us that this company was stationed at Cape Girardeau, Cape Girardeau County, during that time. Those records also state that "this company was in the engagement with Marmaduke's Rebel forces at Cape Girardeau and in the charge for there [perhaps meant "from there"?] to Chalk Bluff on the Saint Francis River" during the period of "March-April 1863" but gives no specific details.
Company K of the same regiment was stationed at Bloomfield in Stoddard County during March and April 1863, and probably also served in the actions against Marmaduke's southeast MO raid. These I obtained from Broadfoot "Supplement to the 'O.R.'" part 2-Records of Events-Vol. 34, pp. 670 and 673.
I found several actions of parts of this regiment at Chalk Bluff earlier in April, but none specifically on 16 April 1863.
The village of Four Mile is located a short distance to the east from Chalk Bluff.
Craig, why do you wish to know this? With more detail perhaps we can be of more assistance.