Is the radical mastectomy a risky thing to do?

Yes, but . . . Yes, but not having a radical mastectomy when it's called for would be far riskier. Any surgery carries risk and a mastectomy is no different, but those risks are far smaller than the risk of a spreading breast cancer. By the way, if you're concerned that a radical mastectomy is more than you need for your cancer, you can and should always seek a second opinion.
Usual surgical risks. Every surgery has risks, and a mastectomy would carry those risks whhich include the risk of bleeding and infection. Mastectomies are relatively common surgeries and the complicaion rate is low.