Minor maintenance
If you can do the repair by hand without any lathe, with some wax paper, then go for it. It is easy to control the situation if the butt is not spinning at high speed in a lathe. It will be safe, it may even work well enough to satisfy you.
There is a point where you have to decide what is minor. You were given good info from others above this post. The job does require an adequate size lathe to turn the butt between centers, and you will need an adapter made to fit your pin size that will cost more than the repair would cost to have done professionally. And if you hit the finish, and damage it while burnishing the linen . . . ouch! There goes another hundred bucks at least to refinish, and now you need a new linen wrap done after the refinish job. So we are at $150.
Am I trying to scare you? Yes, unless you truly love working on cues and want to take the leap, then: welcome!