In the context of ultrafast spectroscopy, the availability of few-femtosecond UV pulses is key to disclose the role of electron dynamics in photo-activated biochemically relevant processes. Here, we present an optical setup for the generation of UV pulses spectrally tunable between 270 and 350 nm with transform limited durations of 3.0 and 2.9 fs, respectively, and repetition rates up to 50 kHz, using resonant dispersive wave (RDW) emission in an argon-filled hollow-core fiber. The RDW emission is driven by 1030 nm sub-20 fs pulses produced by post-compressing an Yb-based laser with a dispersion-engineered multi-pass cell (MPC). The combination of an MPC with a capillary constitutes a compact source to deliver few-femtosecond UV pulses at high-repetition rates, which is ideal for statistically demanding experiments in molecular physics.