The key is that you are requesting elective surgery, and any avoidable risk should be avoided! Any operation requiring a general anesthetic has the potential for numerous risks, the majority of which are extremely small risks, but risks nonetheless! A cold increases these risks, which include, but are not limited to, aspiration pneumonitis, pneumonia, laryngospasm with loss of airway, increased potential for bleeding due to increased coughing, increased risk of tearing the abdominal muscle plication sutures (causing hernia or worse) due to increased coughing, increased risk of infection, as well as a longer, more rotten-feeling recovery! Having even a mild active viral or bacterial infection--including the common cold-- increases every one of these risks! Even a one-hour breast augmentation would be ill-advised; certainly a multi-hour lower body lift during a cold is just plain stupid! Which of those increased risks sounds good to you?
Having your period is not an issue, though it is certainly easier to have elective surgery the week after your period, rather than just before--you will experience less swelling, bruising, and discomfort, and this can range from minimal difference to a really noticeable difference. But, there is no increase in risks as above!