Does the amount of air noise generated by a portable fan depend on blade design?
It's more about the blade speed than it is the shape. The blades in common fans are not highly engineered airfoils, so I don't think you'd find one with an especially quiet profile. Though from an engineering perspective, that is possible, I just don't think you can find it in portable household fans. This article describes sources of noise in fans http://www.comairrotron.com/acoustic-noise-causes-rating-systems-and-design-guidelines, and also lists how fans are rated for noise. Perhaps searching on those terms will point you to quieter options.

For a given amount of circulation, choose the largest diameter fan that is acceptable for your purpose, and run it at a lower speed. At lower speeds you should also find any vibration noise minimized, but you can still isolate it from its supports. Such as placing it on a soft rubber mat for a portable fan.