Are smaller regional aircraft safe?

Yes. The high safety record achieved by regional airlines equals that of the major airlines. Jet engines power all regional aircraft, whether a turbo with propellers on the outside-or a turbofan with fans inside the engine casing. Turboprops are well suited to regional flights. They are designed to fly shorter distances more economically than large jets. Regional airlines operate under identical FAA regulations and safety standards as major airlines - including pilot training and rest requirements, safety equipment, and dispatching procedures.
See the Regional Airline Association website.