Hey CC7, welcome to the forum.
I doubt you could replace the spring with the carb bolted to the engine. I'm not saying it can't be done but I would not try it myself. It would take much more time than if you removed the carb and/or the air horn. But the spring might still be there, just loose because someone loosened the small screw on top and did not "hold" the adjustment while doing so.
Any specific reason you want to replace it while it's on the car ? By the way, what is the number on that carb ?
Frank.