I suggest using Gorilla Glue 51ml Clear Bottle to glue the hook and the clear plastic sleeve back onto the blinds winding mechanism. Just make sure to position the hook exactly the same way as the unbroken one. Once the glue cures you can then hang the winding arm back on. Carefully test to make sure the assembly is in good order.
Let me tag our experienced member @Noyade for their recommendations.
If you need further assistance, please let us know.