We discuss a novel approach, based on spectral density reconstruction techniques, to circumvent the well-known problem of analytic continuation from Minkowskian to Euclidean time of electroweak amplitudes above kinematic thresholds. The method can be used to compute any hadron-to-vacuum QCD matrix element involving two external currents and, in its basic form, relies on the use of Feynman's $i\varepsilon$ prescription to regularize the problem. The approach is discussed in the specific case of radiative decays of pseudoscalar mesons $P\to\ell\nu_{\ell}\gamma$, where $\gamma$ is a virtual photon. These processes, which give access to the rare $P \to \ell \nu_{\ell} \bar{\ell}' {\ell'}$ decays, are notoriously difficult to study on the lattice because of the presence of intermediate states that hinder analytical continuation when the off-shell invariant mass of the photon is greater than that of the lightest intermediate state. We present the numerical results of our study in the case $P=D_{s}$.