The ornamental design for a wall-mounted cooler drying rack, as shown and described.
FIG. 1 is a front view of the wall-mounted cooler drying rack embodying our new design,
FIG. 2 is rear view thereof,
FIG. 3 is a right side view thereof,
FIG. 4 is a left side view thereof,
FIG. 5 is a top view thereof,
FIG. 6 is a bottom view thereof,
FIG. 7 is a perspective front view thereof; and,
FIG. 8 is a perspective front view of the wall-mounted cooler drying rack, the chest cooler shown in phantom comprising no part of the present invention.