There's a glue called "shoe goo" that worked well for me to bond a rubber insole to the sole of a running shoe. The sole isn't cork, but it's a rough fabric that has a similar texture.
If I were you - I might try a different solution: shoe inserts. I'd google and read Amazon reviews to find the best ones. But I wouldn't buy anything from Amazon. Once I knew the brand names - I'd go to mall with a bunch of places that likely sell the inserts. As needed - I'd go to one store after another to get a friendly store clerk to let me open the pack and try them out by walking around.