there is a word наглый which means 'cocky', sometimes 'rude',
you can say самоуверенный meaning 'self-confident', overly confident

беззастенчивый means 'he is never shy', бесстыдный или бесстыжий are used to refer to a person who has no shame - not exactly for the circumstances described

as for successful, it goes like that:

успешный бизнесмен - successful businessman , works in your case

удачный момент - a lucky moment, lucky occasion, convenient time, etc. cf - удачный год = successful year

преуспевающий - doing well, like преуспевающее предприятие - the enterprise which is doing well... might work with your businessman case

удачливый человек - a lucky person, удачливый is always a person who has luck