If it's "double-acting" baking powder, the difference is in the activation with heat. Since you'r recipe called for baking soda, there's likely an acid ingredient of some sort, lemon juice, etc. That causes a reaction at room temperature to release carbon dioxide and lighted the dough. Baking powder has it's own acid included with the soda, so it works in recipes with no added acid. The double-acting kind has an additional acid that's activated by heat, causing a second release of carbon dioxide in the oven. In that kind of cookie, it's unlikely to cause any serious problem. Trying to correct it now is pretty unpredictable, but I'd go with the previous advice and add more baking soda. Baking powder is mostly tartar. You have so far only added 1/3 tsp of baking soda. When the correct amount of baking powder is substituted for baking soda, the final difference is mostly in the flavor. I have no idea of what this will mean in terms of trying to add it now. Might be better to just let it go. I could see it being a mess trying to completely distribute more baking soda into chilled dough.
"Kitchen duty is awarded only to those of manifest excellence..." - The Master, Dogen