How do you train parrot not to fly away and let them stay on shoulders or hands freely without cutting their wings?

You will have to spend a lot of time with your parrot, parrots have to become tame and that will probably be the only way to get them to stay on shoulders. Clipping their wings are to be safe, To do that, just open the wing and cut all the primary feathers, the longer flight feathers, but leave the three outer feathers so when the wing is folded it looks normal.