Integrating microphone arrays into head-worn devices, such as augmented reality (AR) and virtual reality (VR) headsets, as well as hearing aids, has become increasingly popular for capturing and reproducing acoustic scenes. A common requirement in many such systems is a dense set of array transfer functions~(ATFs). However, dense ATFs are cumbersome to measure, and practical setups commonly yield sparse grids rather than the uniform dense sampling often required. This motivates the use of interpolation to reconstruct dense ATF sets from sparse measurements. This paper evaluates spherical harmonics and natural-neighbor interpolation, each combined with onset-based time-alignment and post-interpolation magnitude correction, for a head-worn array across sampling densities. To examine how interpolation errors propagate to binaural rendering, the interpolated ATFs are substituted into two recent filter design methods: signal-independent binaural signal matching (BSM) and a signal-dependent method combining COMPASS parametric spatial coding with BSM (COM). Results show that BSM remains largely robust to interpolation errors, while COM substantially degrades under sparse sampling conditions with errors comparable to BSM at the lowest density, but achieves considerably lower errors than BSM as the sampling grid density increases. This is because BSM averages errors across all steering directions, while COM relies on individual steering vectors for source-directed beamforming.