The letter I in schnappi just gives it a nickname to make it sound better ... When you know many Germans who are familiar with each other, you can add an I when addressing them, of course, when addressing yourself.
Schnappen as a verb is to seize (an opportunity), seize. Catch. Capture. Hold on tight. Personally, I think it is very consistent with the movements and feelings of the little crocodile, which is the place of expressiveness.