Ganesh,
No, it won't "burn thru" the base metal if you get going and move around the edge of the hole (assuming good metal and proper welder setting). It's just like doing the edge of a lap joint, just going in a circle.
From your question you have not done this before. Practice is the key to welding. Either size punch will work. Get some scrap metal, drill a dozen holes of both sizes, clamp the sheets together and practice.
Everyone has their own method. I like to strike the arc on the base metal then go out to the hole edge and run around the hole, then pull back in and fill the center if needed. With a little practice you will have a strong bond and flat surface with little grinding to do.
Remember to move your clamps to each hole because any space between the two sheets will allow things to get too hot and burn back the edge.
Paul