What safety rules apply to coxswains at a regatta?

Coxswains are members of the crew, and any reference to rowers in the Rules includes coxswains unless stated otherwise (Rule 29.1). So these apply to them:

• Swimming: all rowers in an RA regatta must be able to swim 50 m and keep their head above water unassisted for three minutes. The club or school must certify this and provide evidence if RA asks. At the Australian Masters Rowing Championships and the Australian Coastal Rowing and Beach Sprints Championships the individual rower is responsible.
• Pre-existing conditions: any condition that may incapacitate a rower during competition or training must be notified to the Event Medical Officer before racing.
• Briefing: each club, school or Member Association must have at least one person (competitor, coach, manager, etc.) at the Competitors and Coaches Briefing and pass on the racing and safety information to its rowers and coaches.
• Instructions: rowers and team officials must follow Jury and Organising Committee instructions on safety.
• Jury power: any Jury member may prohibit a crew from going on the water if they consider it a danger to itself or other crews. If there is a dispute, the President of the Jury decides.
• Training hours: training happens only during the official training hours, and all crews must be off the water by the closing time. Crews may be sanctioned for not following this.
• Delays: if a race is delayed, crews must ask a Jury member about changes before getting out of the boat.
• Coaching devices: giving instructions, advice or directions to racing crews from outside the boat with any electric, electronic or other technical device is prohibited (Rule 81).

Sources: Rules 29, 63, 81 and the By-Laws to Rules 22 and 63.