And here is my result. You can notice a contour as well, which I do not want either (it may be a consequence of the blurring).
Sorry for necroposting but I believe there is a possible solution for the contour issue.
This works with transparent PNG images (using "indexed color").
You need to set the "matte color" to "none".
In Photoshop this is achieved by going to "Save for the web" => "PNG-8" => "Matte" => "None".
Good luck!