The ornamental design for a removable, cooler-mounted bottle opener, as shown and described.
FIG. 1 is a perspective view of a removable, cooler-mounted bottle opener, the broken line showing of environmental matter being for illustrative purposes only and forming no part of the claimed design;
FIG. 2 is a front elevational view thereof;
FIG. 3 is a rear elevational view thereof;
FIG. 4 is a left side elevational view thereof, the right side elevational view being a mirror image thereof;