Yeah, I thought of plugging in headphones to the gamepad, and yes it does work, I was playing ZombiU (btw i'm amazed at how underrated this game is!!); but I've heard that certain games, in particular Pikmin 3 and Wind Waker - so it isn't ideal.
The item in the link may be the answer, but the oddity is that my monitor does have speakers. I've seen those converters but people seem to be saying that they allow you to receive sound from external speakers, but my speakers are internal... is it the same issue do you think?
Anyway using headphones is a good enough in the meantime and I certainly won't be returning my console, I love it already.