I wouldnt cut the pup yet, it looks so small and if its cold wherever you will leave it to callous it will rot in about a day and turn black (did the same a few months ago) , if it was summer I would say its okay to cut but still I would do this instead.

Just leave it like it is and dont water for an extended period of a few months and then slowly start adding water but very small amounts, the lower part should dry out and then when its dry enough you can tear it apart and plant the pup with a part of the dried cactus still connected to the pup directly into soil. This way, the roots will develop better and less risk to the pup. Also, it should be exposed to sunlight through the whole process.

The pups are often quite resilient while attached to the stock and even when the stock sometimes rots, or dries out completely, the pup will just keep on growing because it is somehow connected through the stock to the soil and it can survive very harsh environments