Paediatric hydrocephalus is a serious medical condition characterised by an excess of cerebrospinal fluid (CSF) in the lateral ventricles of the brain. CSF is produced by the Choroid Plexus (CP) tissue, a vascularised fin-like structure rooted to the bottom of the ventricles. A common treatment for congenital paediatric hydrocephalus is the insertion of a shunt system containing a ventricular catheter, a hollow tube with inlet holes arranged in the tube wall close to the closed tip. Shunt systems run the risk of the CP occluding the catheter holes during drainage, causing it to block and require replacement. While various catheter geometries have been proposed to minimise blockage risk, there is no clear evidence of the relative efficacy of different designs. We present a computational fluid-structure interaction (FSI) model combining open-source OpenFOAM with in-house software MuPhiSim, which simulates the deformation of the CP in an idealised ventricle-catheter environment. The resulting FSI model provides a framework to test the efficacy of different catheter designs, with catheters that cause less deformation of the CP being considered more successful. We demonstrate how key parts of the domain can be identified to form reduced models, which are mechanistically informative, and far faster to evaluate than the full FSI. These models are combined into a surrogate fitness function which is leveraged in a comprehensive optimisation over the catheter design space. Promising candidates identified in the optimisation are simulated in the full FSI environment and shown to be an improvement on existing designs in clinical use.