In fact it is as follows: the size of moving object along it's trajectory measured by stationary observer is less than the size measured by co-moving observer. If I fly past you, I will seem somewhat "flattened" to you, but in my point of view I will be okay (more than that, it will be you, who will look like contracted to me).
As for the Sun, yes, it's "ecliptical" diameter (meaning the diameter parallel to ecliptic plane) measured by you will be less than any other diameter. Or, more precisely, would be, if not for centrifugal "bulges" on it's equator (which is almost parallel to ecliptic plane if I'm not mistaken).
However the effect will be too small, because the Sun's velocity relative to the Earth is only 30 km/sec, which is almost nothing compared to speed of light in vacuum.
ADD: not one-tenth, but one per ten thousands (0.0001)