I would use After Effects or Premier pro.Take your 4:3 clip and add it to a sequence that has the same settings for everything except the aspect ratio, which should be set to 16:9. If the clip interpretation settings are correct when you add it to the sequence it should sit in the middle of the frame with black on either side.Create a second video layer and duplicate the clip into the new layer, making sure you don't shift the timing of the clip.Open the scaling settings for the lower clip. This will be in the transform controls. Uncheck the 'constrain aspect' option, so you can scale the width separately from the height. Scale the x value until the clip is stretched to the edge of the 16:9 frame.You should now have a streched version of your clip undeneath the original version of your clip.Add the blur effect to the stretched layer and adjust it to taste.This should only take a few seconds to setup once you are familair with the process. I'm sure there are automated solutions out there too but this is how I would do it.