sometimes there are multiple componants that fit inside one cutline, so I copy the whole design to the clipboard, then select all & change to black fill, black stroke, then object>path>outline stroke, then in the pathfinder dialog box, choose Unite to weld it all together. This creates a perimeter contour like you would have on your examples outer-most contour if the multiple elements overlap each othr. If they dont, at this point, I would convert the fill to none, & the stroke to black... then I would increase the stroke width, until the strokes of my non-overlapping contours are overlapping. I would make sure my stroke options are set to rounded corners, then I would repeate the object>path>outline stroke command and then convert the fill to none, & the stroke to black again. Then I "paste-in-front" the original artwork which should center it right where it was. If the cut line got too far from the art, I'd repeat the outline stroke process to create an inner contour thats the right distance from my art.