Unless you have a macro routine I am afraid there isn't anything like you described.
I feel your pain and it would be nice if there was such a thing. You are best to just
delete all of these sements and draw in your spline curves.
Now what might be a way to do it is import this into a drawing and make a block out of it
then create a sketch over it. Like tracing over it.
Hope this helps.
The tool is called "fit spline" and it tries to fit a spline over any closed set of lines you select. Unfortunately, your imported lines probably don't have line segments that all have merged endpoints, but it is worth a try. I suggest importing that logo into a new part file, into a sketch on a plane. Then try and fix it up there, before you copy it into a drawing.