Accurate measurements of electron density in irreproducible microscale high-density plasmas are indispensable for improving laser processing and plasma processing technology because the dynamics of these plasmas are strongly influenced by their electron density. Because single-path laser wavefront sensors are capable of acquiring the two-dimensional electron density distribution with a single shot, the electron density of irreproducible millimeter-scale low-density plasmas has been measured by using such sensors. However, the strong diffraction effects caused by the irreproducible microscale high-density plasmas pose challenges for the measurement. In this study, we numerically and experimentally demonstrate a suitable optical configuration of single-path laser wavefront sensors for accurate measurements of irreproducible microscale high-density plasmas with minimal measurement errors. Our Fresnel diffraction-based numerical simulation indicates that the serious measurement errors caused by the strong diffraction effects can be significantly reduced through the use of relay lenses with high magnification and a short-wavelength laser source. In addition, we propose an alignment procedure for the optical setup to minimize the measurement errors and experimentally validated the procedure by measuring a laser wavefront shaped by a spatial light modulator. Finally, we applied the verified laser wavefront sensor to the measurement of a laser-induced plasma with a two-dimensional line-integrated electron density higher than 1 x 10(21) m(-2) in an approximately 40 x 50 um region. This study provides a new strategy to rigorously analyze the dynamics of irreproducible microscale high-density plasmas using a laser wavefront sensor.