Displaying "Site Stats logo" is optional since ages ( http://adwords.blogspot.hu/2008/09/conversion-tracking-site-stats-logo-is.html ).
You can modify the "Tracking Indicator" setting of the existing conversion to "Don't add a notification to the code generated for my page." and generate a new tracking code.
The only difference will be in the following line, this way you can change all your conversion codes in bulk:
var google_conversion_format = "2"; // WITH Site Stats logo
var google_conversion_format = "3"; // WITHOUT Site Stats logo
Hope this helps, feel free to ask.
