If it was me I wouldn't hesitate getting the Sigma 8mm f/3.5 Fisheye. 4 shots at 90 degrees tilted up 4 degrees will fully close the top/ceiling/zenith hole and the tripod/panohead/floor/nadir will need to be capped or cloned as it would in any other solution. Of course you make choose to shoot a nadir image to help with patching hand held.
No images regardless of the lens once stitched will give a distorted image (that is a myth that newbies always have a concern about) If you see distortion in a panorama it is because the viewing FOV (Field of View) in incorrectly set allowing you to see more than the human eye expects.
There is no risk that skill in Photoshop will be of benefit along with knowing the camera and equipment being used.
Look around and learn more before buying your equipment. But let others guide you as it is a well warn path. What is your budget and what do you own so far?