I don't recall ever replacing the firing pin on a Rossi, but AFAIK you are correct that it is like the S&W. With the right equipment, the job can be done without even removing the hammer from the frame, but in general it is best to do so. Then you put the hammer down on the steel bench block with the rivet over the appropriate hole and use a small punch to drive out the rivet. If you have also ordered a new rivet (as you should have), just replace the firing pin, install the new rivet and use a cone shaped riveting tool to expand the rivet. If you don't have a new rivet, file down the old one until it will go back in. If you don't have the tools, they can be made or bought, but it might be easier to have a gunsmith do it if you have a good one at hand.
Jim