Whatever mechanical means you use, floss, fishing line, thin plastic blade, etc, make sure the paint around the badge is perfectly clean. Any little abrasive grit will scratch the paint once you loosen the badge. Also, consider using soapy water as a lubricant.
You can remove the old adhesive from the badge and apply new adhesive. I no longer "spam" the board with recommendations regarding adhesives but I will say it's generally easier to get new badges. If you look at your old badges closely you may find they look quite weathered with dull chrome plating. New badges are pretty inexpensive.