Capillarity-driven self-assembly of small chips onto planar target substrates is a promising alternative to robotic pick-and-place assembly. It critically relies on the selective deposition of thin fluid films on patterned binding sites, which is anyway normally non-conformal. We found that the addition of a thin wetting sidewall, surrounding the entire site perimeter, enables the conformal fluid coverage of arbitrarily shaped sites through dip-coating, significantly improves the reproducibility of the coating process and strongly reduces its sensitivity to surface defects. In this paper we support the feasibility and potential of this method by demonstrating the conformal dip-coating of square and triangular sites conditioned with combinations of different hydrophobic and hydrophilic surface chemistries. We present both experimental and simulative evidence of the advantages brought by the introduction of the wetting boundary on film coverage accuracy. Application of our surface preparation method to capillary self-assembly could result in higher precision in die-to-substrate registration and larger freedom in site shape design.