A bag of ice cubes is $3 here and I simply dump them out of my cheap Coleman cooler after the fish have been cleaned. I'd rather not spend the time and effort of cleaning ice packs of various sizes plus the related hidden cost of the electricity of freezing them all again.
One thing to think about is how many you're taking at a time and getting a cooler big enough that you have good surface contact between the cold surface and the fish. Mine is a bit on the small side and I often have to shake it around a bit to rotate the fish down into and around the ice. Otherwise the ones on the bottom are on ice and everything above that is simply stacked together and not getting cooled. They stay warm and will soften; I learned about that kind of early on.
Yes, I was talking to myself; sometimes even I have to ask for expert advice.