I’m not sure what your issue is…it looks like you have a 40mm axle which would mean your kart has 40mm bearings. Do you want to convert the kart to a 50mm axle? In addition to the larger diameter axle you will need 50mm bearings as well as a brake hub (which may or may not work with your brake rotor) and sprocket hub. The keys should be specific to the axle as they are usually pinned and the spacing can be different. However, most keys should work with different brands of hubs. The hubs you have are fairly long and you may have a hard time on a full length axle getting the rear end width correct. if that is the case you could use a shorter hub or cut some of the length off the end of the axle.
Your other option is to stay with the 40mm axle and just find hubs that are 40mm.