Kitchen Large Electric Appliances - reinstalling broken door shelves

I bought new pick off hooks and rivets for my 2 broken Maytag refrigerator door shelves. Attempting to intall the rivet into the hook, I destroyed the first rivet which is supposed to secure the pick off hook onto the shelf itself. Is there a special tool I should be using to force this rivet into the hook? I need to apply force to the rivet and an opposing force to keep the hook in place. It's much more dificult than I expected. The shelf design gives very limited space on the hook side, but the rivet side is well exposed. Any ideas? Luckily I bought an extra rivet, but I have to get 3 out of the next 3 rivets right or I'll be emptying my bank account again paying big bucks for what should be 25-cent platic parts. Thanks!