Right after opening my map, an error appears: "Invalid or corrupted skin."

Please edit your report to change the Affected Version to the version shown on the Minecraft title screen

The error message shows that you are running version 1.21.113 (not “Future Update”).

Please update to the latest release 1.21.114 and check if the issue still occurs. Please let us know either way what happens.

Please also try picking a different skin from the dressing room to see if that helps.