Hi Polly
That's just what I do, except that ice is TOO cold, so I use cool water which has been in fridge overnight and discard from from thermos flask at security check. Then add cool tap water on other side, if it's available. Some people use Frio packs, but I find a small stainless steel flask is much cheaper, more versatile (can use it for carrying hot drinks once insulin is safe in shade / fridge at destination) and offers more physical defence for insulin against breakage from knocks / squashing etc.
Check you patient information leaflet, but most insulin is OK to be kept at room temp (assumed to be not lower than 0oC, which is colder than fridge, and not higher than 28oC) for 28 days, regardless of whether cartridge has been opened or not.