General Synonyms:
* Administrative
* Executive
* Supervisory
* Leadership
* Directorial
* Controlling
* Guiding
More Specific Synonyms:
* For "managerial skills": Leadership skills, organizational skills, communication skills, problem-solving skills, decision-making skills
* For "managerial role": Executive, supervisor, leader, director, administrator, head
* For "managerial style": Autocratic, democratic, laissez-faire, transformational, transactional
The best synonym to use will depend on the specific situation and what you are trying to convey.