Multimode fibers (MMFs) show great promise as miniature probes for sensing, imaging, and spectroscopy applications. Different parameters of the fibers, such as numerical aperture, refractive index profile and length, have been already optimized for better performance. Here we investigate the role of the core shape, in particular for wavefront shaping applications where a focus is formed at the output of the MMF. We demonstrate that in contrast to a conventional round-core MMF, a square-core design does not suffer from focus aberrations. Moreover, we find that how the interference pattern behind a square-core fiber decorrelates with the input frequency is largely independent of the input light coupling. Finally, we demonstrate that a square core shape provides an on-average uniform distribution of the output intensity, free from the input-output correlations seen in round fibers, showing great promise for imaging and spectroscopy applications.