This is a good point. In fact, you would probably be in breach of digital copyright law if you sent the library, with attachments, to someone at another institution. Many of your attachments would have been obtained from databases to which your institution subscribes, and it is illegal (however commonplace!) to send such material to somebody who is not attached to your institution.
I think there is a fairly easy workaround. The attachments are not stored in the .enl file, but in a folder within the DATA folder. So, in Windows Explorer or My Computer, make a copy of the .enl file and give it a new name. Then go to EndNote and open the new .enl file. EndNote will create a DATA folder for the .enl file, but of course the DATA folder will not contain the attachments. So if you try to open any of the attachments from the new library, you will get an error message. You can compress the new library, and send it to a colleague, with an explanation that the attachments are not included.