There is a plethora of cushioned products available online for this purpose if you do not want to make permeant alterations. Try an internet search for "Corner Guards" or "Corner Cushions for Furniture", or "Baby Proofing Corner Guards". Some are just corners that slip on and others (like one from "Safety 1st" and "Roving Cove") have a range of colors and can be applied on the corners and all the way around for improved aesthetics. My choice of this kind of fix would be the clear corner only type protectors from UXU
(like these).
Considering what tools I have available and my comfort level in using them, for a more invasive, permeant fix, I would mark a radius on the corners and use a jigsaw and sander to first round them. I would then follow up by rounding the top edge all the way around the top with a bearing guided round over bit in my router. If done carefully, I think the result could possibly be masked off and finished with a few coats of brush on lacquer. Otherwise, the entire top would need to be sanded down and re-finished. (I think I would first take the less permeant approach to see how it worked out).
Good luck!
Dave