When you just mix the two parts they are the most stickiest. Try to wait for some 10 minutes or so, it will become less sticky and more workable. But mind the time though as if you are too slow, it will be hardened. I personally think that the best handling time is about 30 minutes after you mix, but it gets stiff and less manageable for minute details. Or if you must take longer working time and start right after you mix, put some (very little but even) vaseline on your fingers. It will prevent the sculpt from sticking to your fingers. Practice more and you will get some sense of it. And try small portions at a time. Good luck.
To smooth the putty before it fully cures, just smooth it with wet fingers, I prefer this to sanding after it hardens, as sanding gives different depth to different material (for example, you patch on plastic or rubber, and when you sand, it will worn at different degree leaving you with an "edge".) So I think it is best to smooth/blend the putty into the surrounding when it is still soft.