Your surgeon likely would not proceed with your operation if (s)he did not think that it is safe to proceed. Thalassemia trait may not manifest in any significant increase in bleeding risk, or could mildly elevate your risk, but most operations can still be performed safely. Good attention to hemostasis is key in all operations, and even with attentiveness, bleeding and hematoma can occur on occasion. If your preoperative hemoglobin is over 11, most surgeons would be comfortable proceeding. Obviously this needs to be considered in the context of your overall general health and any specifics to your case need to be reviewed with your surgeon and hematologist/PCP as appropriate.