Color accuracy does not depend on the GPU at all. It is only dependent on the quality of the LCD screen itself. There is color accuracy where the colors only need to be good enough given the price of the laptop and the hobby you want to pursue. Then there is "COLOR ACCURACY" where we are talking about professional work where color accuracy is extremely important.
In either case you are not going to find a laptop with decent color accuracy within your budget because it is too low. A $350 laptop has to cut a lot of corners to bring the price down that low. That means low performance hardware and relatively low quality LCD screens. The cost of a color accurate LCD display panel alone used in a laptop for professional graphics purposes can...