Speaker or line-out jack...

Docedison:
Quick one word answer NO. you have 4 wires that need to go to the jack... not counting the ground. Line out, the unswitched output and the connection to the volume controls that you are switching with the jack. You could of course use a DPDT mini toggle switch. That would take care of the audio switching necessary... But it won't happen when you insert the plug... You could use the mono jack to activate a relay... but that meqans that if you loose the plug (Shorting plug to "switch on the relay...) But If you lost it... No Switch. Here is an inexpensive one from a place I spend money at (Lots of Money, they have Lots of inexpensive Goodies)
20PCs 3F07 Dual Channel Audio Socket 3.5mm - ElectroDragon... The Part is PCB mounted only But it is $0.21... Most all of what they sell is in that class.

Doc

Well there are just 2 wires. I need no volume control, as that would be in the output.
What I have is something looking like this:

On the main view, isn't there an easier solution than adding IC's or relays?...
To Magician, I am not using Arduino on this project. Otherwise it'd be much easier, of course.