We experimentally demonstrate spectral broadening and shaping of exponentially-decaying nanosecond pulses via nonlinear mixing with a phase-modulated pump in a periodically poled lithium niobate (PPLN) waveguide. 1550 nm pump light is imprinted with a temporal phase and used to upconvert a weak 980 nm pulse to 600 nm while simultaneously broadening the spectrum to that of a Lorentzian pulse up to 10 times shorter. While the current experimental demonstration is for spectral shaping, we also provide a numerical study showing the feasibility of subsequent spectral phase correction to achieve temporal compression and reshaping of a 1 ns mono-exponentially decaying pulse to a 250 ps Lorentzian, which would constitute a complete spectrotemporal waveform shaping protocol. This method, which uses quantum frequency conversion in PPLN with >100:1 signal-to-noise ratio, is compatible with single photon states of light.