Ultrafast laser pulses that are both tunable in wavelength and very short in duration are essential tools in fields ranging from biomedical imaging to ultrafast spectroscopy. While resonant dispersive-wave emission in gas-filled hollow-core fibers is a powerful technique for generating such pulses, it has traditionally required complex and expensive pump laser systems. In this work, we present a more compact and accessible alternative that combines gain-managed nonlinear amplification with resonant dispersive-wave emission. Our system produces sub-20 fs pulses tunable from 400 to beyond 700 nm, with energies up to 39 nJ and peak powers exceeding 2 MW, operating at a 4.8 MHz repetition rate. This compact and efficient laser source opens new avenues for deploying resonant dispersive-wave-based technologies for broader scientific and industrial applications.