Josephson parametric converters (JPCs) are superconducting devices capable of performing nondegenerate, three-wave mixing in the microwave domain without losses. One drawback limiting their use in scalable quantum architectures is the large footprint of the auxiliary circuit needed for their operation, in particular, the use of off-chip, bulky, broadband hybrids and magnetic coils. Here, we realize a JPC that eliminates the need for these bulky components. The pump drive and flux bias are applied in the Hybrid-Less, Coil-Less (HLCL) device through an on-chip, lossless, three-port power divider and an on-chip flux line, respectively. We show that the HLCL design considerably simplifies the circuit and reduces the footprint of the device while maintaining a comparable performance to state-of-the-art JPCs. Furthermore, we exploit the tunable bandwidth property of the JPC and the added capability of applying alternating currents to the flux line in order to switch the resonance frequencies of the device, hence demonstrating time-multiplexed amplification of microwave tones that are separated by more than the dynamical bandwidth of the amplifier. Such a measurement technique can potentially serve to perform a time-multiplexed, high-fidelity readout of superconducting qubits.