Can you picture what you expect the result to look like? If you don't want the adjacent edges affected at all the radius would need to taper out on both sides before it reaches the ends of your blue line. This could be accomplished with a variable radius fillet.
Or do you want it to "tear away" from the adjacent surfaces, like this?
I don't know of an easy way to do that, the way I did it was kind of complicated. If that's what you are after I can explain but I have a feeling it is more work than just deleting and recreating the adjacent faces.
Could you not add the fillet radius before the side surfaces are created?
If you make the part solid first, you could use a cut-extrude instead of a fillet, or you could split the part, add a fillet to the centre body & then combine.