Fast (nanoseconds) optical wavelength switching is emerging as a viable solution to scaling the size and capacity of intra-data center interconnection. A key enabling technology for such systems is low-jitter optical clock synchronization, which enables sub-nanosecond clock and data recovery for optically switched frames using low-cost methods such as clock phase caching. We propose and demonstrate real-time low-latency wavelength-switched clock-synchronized intra-data center interconnection at 51.2 GBd using a fast tunable laser (with ns scale switching time) and ultra-stable-latency hollow core fiber (HCF) for optically-switched data center networks. For wavelength-switched systems, we achieve a physical layer latency below 46 ns, consisting of 28 ns transceiver latency and a 18 ns inter-packet gap. Finally, we show that by exploiting the low chromatic dispersion and thermally-stable latency features of HCF, active clock phase tracking can be entirely eliminated.