I found this recommendation from a research study of radial scars. Based on this, it sounds as though complete excision would be a good idea:
"A percutaneous diagnosis of a radial scar does not exclude associated malignancy at surgical excision. Mammographic and sonographic features of a lesion diagnosed as a radial scar at percutaneous imaging-guided biopsy do not predict which lesions will have associated malignancy at surgery. Therefore, all patients with percutaneous diagnosis of a radial scar should undergo surgical excision regardless of mammographic and sonographic appearances, until further criteria can be determined."
In regard to whether having had a RS raises your furture risk, a 1999 study indicated that having a radial scar may increase a woman's risk for BC two-fold, but a 2007 report that concluded that RS imparts no increased breast cancer risk above that of women who had proliferative disease without atypia (PDWA) or atypical hyperplasia (AH), without RS.
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Best wishes...
Radial scar is not a scar at all, but a benign lesion of the breast made up of fibrous and glandular tissue.
There has been one study that suggests that the presence of radial scars may increase the risk of developing breast cancer.This is especially true in women with other risk factors.
Radial scars are often excised to exclude malignancy,because it has the appearance of a star-shaped density that shows up on X-rays and which may, in a handful of cases, be hiding a cancer.However, observation following a core biopsy may also be considered.
A study done by Jacobs, (see http://content.nejm.org/cgi/content/full/340/6/430) showed that women with radial scars have a risk of breast cancer almost twice that of women without the condition.It is important to understand that radial scars are just a "marker" of increased risk for breast cancer.It does not by itself cause cancer.
Since both your Radiologist and your Surgeon have different opinions,I would suggest to seek a third opinion from another radiologist or a breast specialist so you can make a better decision.
Best wishes...