The Hi-Lumi Upgrade to the LHC will utilise crab cavities to increase the peak luminosity and provide luminosity levelling at the increased crossing angle. A transversely compact design is required to fit within the limited space between opposing beamlines. In this paper, further design work for a four rod TEM deflecting cavity (4RCC) is shown to be suitable for LHC. The variation of the deflecting voltage with radial offset has been minimised by careful design. An aluminium prototype has been constructed and the bead pull measurements are compared to simulations. Multipacting can be a major problem for any RF cavity and simulations have been performed to ensure the shape chosen has a lower chance of strong multipacting, and weak multipacting can be processed through. The final niobium cavity is expected to be held in a helium bath at 2 K, pressure variations can result in deformation of the complex shape which will alter the resonant frequency. Mechanical simulations have been performed to assess the sensitivity of the frequency to cryogenic pressure fluctuations, which are presented. In order to reduce the impact of these cavities on the LHC beam, a low impedance is required for the HOMs as well as the fundamental monopole mode. The couplers for the 4RCC cavity have been optimised to provide effective damping of these modes while rejecting the operating mode.