You may fly without ADSB under the Class B or Class C shelf provided you remain outside of any Mode C veil. §91.225 tells you where you cannot fly. It says you cannot fly within the lateral boundaries of the Class B or C airspace or above the airspace. It does not say anything about under the shelf.

Automatic Dependent Surveillance-Broadcast (ADS-B Out) is a surveillance technology where an aircraft determines its position via satellite navigation and periodically broadcasts it, enabling it to be tracked. While it is mandatory in most busy controlled airspaces (such as Class A, B, and C in the US and much of Europe), there are still areas in 2026 where it is not required. Generally, ADS-B is not required in uncontrolled airspace (Class G) or in controlled airspace that is away from major metropolitan hubs and below 10,000 feet Mean Sea Level (MSL). In the United States, for instance, you do not need ADS-B Out if you are flying outside the "Mode C Veil" (a 30-nautical-mile radius around major airports) and staying below 10,000 feet, provided you are not crossing into restricted or prohibited areas. Many rural strips and remote regions in Africa, parts of Asia, and deep South America still do not mandate this equipment for light general aviation aircraft, although the global trend is rapidly moving toward universal adoption for all powered aircraft.