Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices

•Symplectic integration can be efficient for systems in non-canonical coordinates.•For the method a map to canonical coordinates is required, but not its inverse.•The method applies to guiding-center orbits with appropriate canonicalization.•For nested magnetic equilibria the canonicalization can be efficiently pre-computed.•Computing time for stellarator fusion alpha particle losses is improved by factor >3.