Deleting a 'No such file or directory' file
Removing a .Trashes directory or a .Trash directory is the wrong approach. You want to just remove the files and directories within your .Trashes or .Trash directory. Assuming your shell is bash you can list those file system objects in your .Trashes directory with find. In this example the secondary hard drive is named backup.

find /Volumes/backup/.Trashes/"$UID" ! -name "$UID"


If the results are the files you wish to delete then you can add -delete to the find statement. Please be very careful applying this option.

find /Volumes/backup/.Trashes/"$UID" ! -name "$UID" -delete


For files in your home folder's .Trash directory

find ~/.Trash ! -name .Trash -delete