Positronium in the \(2^3S\) metastable state exhibits a low electrical polarizability and a long lifetime (1140 ns) making it a promising candidate for interferometry experiments with a neutral matter-antimatter system. In the present work, \(2^3S\) positronium is produced - in absence of electric field - via spontaneous radiative decay from the \(3^3P\) level populated with a 205nm UV laser pulse. Thanks to the short temporal length of the pulse, 1.5 ns full-width at half maximum, different velocity populations of a positronium cloud emitted from a nanochannelled positron/positronium converter were selected by delaying the excitation pulse with respect to the production instant. \( 2^3S \) positronium atoms with velocity tuned between \( 7 \cdot 10^4 \) m/s and \( 10 \cdot 10^4 \) m/s were thus produced. Depending on the selected velocity, a \(2^3S\) production effciency ranging from \(\sim 0.8 \%\) to \(\sim 1.7%\), with respect to the total amount of emitted positronium, was obtained. The observed results give a branching ratio for the \(3^3P\)-\(2^3S\) spontaneous decay of \((9.7 \pm 2.7) \% \). The present velocity selection technique could allow to produce an almost monochromatic beam of \(\sim 1 \cdot 10^3 \) \(2^3S\) atoms with a velocity spread \( < 10^4 \) m/s and an angular divergence of \(\sim\) 50 mrad.