A collection of AppleScripts for muting Mail.app threads.
Download and put these into ~/Library/Scripts/Applications/Mail.
Open Script Editor, open its Preferences and enable “Show Script menu in menu bar”.
Download and put these somewhere; ~/Library/Scripts/Applications/Mail is still a great location.
Set up Keyboard Maestro or a similar tool to execute the script on a hot key.
Marking the messages as read is (partially?) broken, so make it also execute “Message → Mark → As Read” as part of the macro. (Disable stop-on-failure, because the command won't always be available.)
For a visual confirmation, you can optionally configure it to display the execution results in a notification.