I have only ever had to source insulin in Europe when I was able to go to a pharmacy and buy direct without a prescription. I did know a type 1 English teacher that was able to do the same in China (but maybe you should check if anyone has any info on the travel forums). If you have the money it seems you can get pretty much anything in a lot of places.
As for keeping insulin cool (which you might need to do) then I can say that I have only ever used a water activated frio wallet for several days - in 25-30c) that seemed to work well (I kept it wrapped up in a toiletries bag out of direct sunlight in the centre of my backpack).
I don't know what kind of plan you have. Obviously if you are bikepacking (like with a tent and cooking equipment etc.) then extra weight MIGHT become an issue for you regarding taking along some kind of 'mini fridge'. Though I presume (again if you have the money) that you can probably get one that is more lightweight than they used to be - the one I still have in the loft IS literally a miniature fridge which I used when I was in a house share back in the day.
As for cycling itself, funnily enough I was only just looking up The European Divide the other day (a 7500km+ cycle route from Arctic Norway to Portugal).