Try removing the .osx extension or replace it with .app and see if that doesn't fix it.
adding .app extension converted it into a file for CLASSIC environment. Thus this does not work.
Did you try removing the extension entirely?
Chances are highly likely that you have lost the resource fork of the executable file when you copied it to the external drive. If it was not formatted as HFS, then it would probably not copy the resource fork. This is a notorious problem.
If you have another copy of that file that still works on a different mac, then zip it. Then copy the zip to your "problem" mac. Unzip it there, and it should work. If you try to copy it to a non-HFS drive (or even if you are using a Non-Mac OS to do the copy), then it will only work if the file is zipped (or archived in some way).
If you do not have a working version of the executable, then you would need to republish it from source in Director.