Does a router smooth edges significantly more than a jigsaw?
Tried to make this a comment but must have been to long. So here goes. 
I think a router would be what you are looking for. There are bits that will cut a 45 and a curved edge. Both will help with the sharp edge. Some bits control the depth with a shaft (cheaper ones) some control with a small bearing. The trick is to figure out the direction of cut to make the cleanest cut, cut two deep and the cut is rough and the router gets away from you. I usually plan on a rough cut to get most of the material off and then a second cut to get a smooth edge. I like carbide bits with a bearing the best but have had good luck with High speed steel on softer wood. A router is great for trimming laminate counter tops so that could be a future project.