Chris welcome to the Seven Forums.
Which would be the best option for replacing this card without huge amount of hassle.
None. It isn't like a desktop where you can just go to any retail or online shop and pick up a video card. In the case of yours it should be socketed and not soldered which means it can be changed, but like I said finding one is another story.
If it really is the card that is failing I would be contacting the laptop manufacturer about a warranty return.