Yes, you should be fine with regular baking powder without changing the quantity...
Here is info on both:
"Single-acting baking powders are characterized by the type of acid they include. Tartrate baking powders contain both cream of tartar (potassium acid tartrate) and tartaric acid. These create gas quickly when combined with baking soda in the presence of liquid, so the batter must be cooked quickly or it will go flat. Phosphate baking powders contain either calcium phosphate or disodium pyrophosphate (source of sodium pyrophosphate). They work a little slower than the tartrate baking powders, but most of the gas is still created outside of the oven and therefore can be lost. S.A.S. baking powders have sodium aluminum sulfate (alum) as the acid. S.A.S. baking powders react slowly at room temperature and release more of the gas when heated. The phosphate and tartrate baking powders react rapidly at room temperature to release the leavening gas, which means that the batter has to be cooked quickly after the liquid ingredients have been added. On the other hand, the S.A.S. baking powders are better for products that will sit a while before being cooked. The problem with S.A.S. powders is that they have a bitter taste. They are used in combination with other leavening agents so not as much is needed. S.A.S. is often used in D.A. powders.
Double-acting (D.A.) baking powders are the most common type of baking powder in US supermarkets. The first "action" refers to the release of gas when the baking soda in the powder reacts with an acidic liquid. D.A. baking powders contain a dry acid which does not react with the baking soda in the powder until water is added; at that point the baking soda dissolves, the acid dissolves, and the two can now mix and the reaction shown above occurs.
The second "action" refers to the release of gas when the batter is heated in the oven or on a griddle. This relies on the presence of the slower acting acid, S.A.S. which only combines with soda when the temperature increases."