It appears that this affair is recorded in the records under a number of names.

May 10, 1864 - Engagement at Cove Mountain, or Grassy Lick, near Wytheville. Skirmish at New River Bridge
http://thomaslegion.net/battleofcovemountain.html

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Numbers 19. Report of Brigadier General William W. Averell, U. S. Army, commanding Cavalry Division.

HDQRS. CAVALRY DIV., DEPT. OF WEST VIRGINIA,

May 23, 1864.

CAPTAIN: I have the honor to submit the following report of the operations of my cavalry division from the 1st instant to the present date: . . . . .

. . . . Arriving near Wytheville on the afternoon of the 10th, I attacked a force stated by rebel newspapers to have numbered 5,000, under Generals Morgan and W. E. Jones, on their way eastward. This force was mostly infantry, with three pieces of artillery, and posted in an admirable position for defense or attack, impossible to turn with cavalry. The Fourteenth Pennsylvania and First [West] Virginia Cavalry, under Colonel Schoonmaker, opened the battle, while the brigade of General Duffie was formed in line of battle; the Second [West] Virginia, under Colonel Powell, on the left, mounted; the Thirty-fourth Ohio Volunteer Infantry, dismounted, on the right, and the Third [West] Virginia cavalry occupying the extreme left. The enemy pressed upon both flanks and advanced in three lines sheltered by fences in front. The field was maintained four hours, the vigor of the enemy gradually decreasing. At dark there was some prospect of our being able to drive him, but after dark he retired, and I marched to Dublin, where I arrived on the evening of the 11th.

Our loss in the battle was about 114 officers and men killed and wounded. (Reports are inclosed.) . . . .

My thanks are due to the brigade commanders and their staffs for their energetic efforts while under my command.

Respectfully submitted.
W. W. AVERELL, Brigadier-General, Commanding.
Captain J. L. DOSTFORD,
Assistant Adjutant-General.

OR V37, Pt. 1, pp. 41/2

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On May 10, Brig. Gen. W.W. Averell’s raiders encountered a brigade under William “Grumble” Jones near Cove Mountain. After delaying the Union advance, the Confederates withdrew. The next day, Averell reached the New River Bridge on the Virginia & Tennessee Railroad, which he burned.
https://www.nps.gov/abpp/Battles/va109.htm

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Fourteenth Pennsylvania Charles C. Coltman & Henry Pflau killed, Dennis Sweeney captured at
Wytheville, Va.
First [West] Virginia Cavalry Gideon Weller killed, Gottlieb Wipf at Wytheville
Second [West] Virginia Sumner F. Chase* killed at Cove Mountain
Third [West] Virginia cavalry
Thirty-fourth Ohio Volunteer Infantry, dismounted Alexander Colwell killed at Cove Mountain, Andrew J.
Rickard wounded at Cloyd's Mountain, VA

* His CSMR records he was killed May 10, 1864 near Witheville [sic] & at Cove Mountain
Shot through left breast near Wytheville, WVa on the 10th day of May 1864

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34th Ohio Infantry - On the 1st of May 1864, the second expedition for the destruction of the Virginia and Tennessee Railroad left Charleston. On the 9th the cavalry arrived at Wytheville, encountered the Rebels under General Morgan, were repulsed, and compelled to fall back, with considerable loss.
http://www.rootsweb.ancestry.com/~scprnyz/ZouaveArchive/UnionZouaves/Ohio/Ohio_34thInfantryRegiment.html

On May 9, the cavalry forces arrived at Wytheville and engaged an enemy force that drove the Northerners from the field
http://www.ohiocivilwarcentral.com/entry.php?rec=1248