We investigate the spontaneous scalarization of generic, static, and spherically symmetric regular black holes supported by nonlinear electrodynamics. Starting from an arbitrary seed metric, we employ the $P$-dual formalism to reconstruct the electromagnetic sector and subsequently couple a real scalar field nonminimally. As a worked example, we apply the framework to the regular Balart-Vagenas black hole, showing that scalarized and scalar-free branches can coexist in a region where the scalarized configurations are entropically preferred. We further assess possible observational imprints, finding percent-level deviations in both the shadow size and the fundamental scalar quasinormal modes ($<10\%$ for small charge-to-mass ratios), indicating that current electromagnetic and gravitational-wave observations do not rule out these solutions. Our construction thus provides a general route to explore scalarization on top of nonlinear-electrodynamics-supported spacetimes, extending beyond specific Reissner-Nordström-like cases.

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• Astrophysical studies of gravity
• Classical black holes
• Gravitational waves