Q: ipod shuffle 3 : impossible to detect it on mac (finder, itunes and disk utility)

Does it still charge when connected?  You said it still works with headphones.

It's possible that the connection port (the headphone jack) on the shuffle has become faulty.  It has different connection points, so it's possible for it to work for headphones (and charging), but not for data.  It's also possible that the USB cable is bad, if you have only one and no alternate way to test it and confirm it's working.

However, you can try these other things.  Shut down the Mac and disconnect all USB peripheral devices, including any hub.  Use this procedure to reset the shuffle

http://support.apple.com/kb/HT1655

Start up Mac with nothing connected, except for standard keyboard and mouse (for a Desktop Mac).  Connect the shuffle to a direct USB port.  Check with iTunes, Finder, and Disk Utility to see if there is any improvement.

If that works better, experiment with connecting other USB device, to see if there was some type of USB conflict, or maybe overloading of USB bus (for power).

I'll try to find another cable to test it.

If it's a 3rd gen iPod shuffle (the one with no control buttons), don't use a USB cable for the 2nd gen shuffle, because they are different.  The stock 2nd gen shuffle cable has a mini-dock at the end, so you probably cannot use it with other shuffles.  However, there are cheaper third-party USB cables for 2nd gen shuffle that just have the connector (no dock).  Those will fit on the 3rd (and 4th) gen shuffle, but it won't work.

If you have an Apple Store nearby, you can make a reservation at the Genuis Bar.  You can have the tech try it on one of their machines with their cable, and that would rule out everything except some problem with the shuffle itself, unless it actually works there.  And if it still doesn't work, maybe they'll have a clue about that too...