To enhance the aerothermal performance of squealer blade tips with minimal geometric modifications, a methodology was proposed in this study for the design of inclined pressure-side shoulder, based on the non-uniform tip profile offset. Utilizing the squealer tip of the first-stage rotor in the GEE3 engine as a foundation, two design schemes of outward and inward inclined pressure-side shoulders were developed. Through the modification of inclination amplitude and shoulder thickness, eight representative shoulder configurations were constructed. The influence on aerodynamic and heat transfer characteristics variation was investigated under turbine stage conditions. First, the reliability of the numerical method was validated against linear cascade experimental data and grid independence verification. Subsequently, computational fluid dynamics (CFD) models were solved to compare the differences in tip leakage flow and vortex structures near the blade tip between outward-inclined and inward-inclined shoulder configurations. Based on flow field characteristics, the mechanism by which inclined shoulder configurations influence aero-thermal performance was analyzed. Finally, the variations in the aero-thermal performance of the blade tip were quantified through total pressure loss, turbine efficiency, and heat transfer coefficient. The research findings indicate that the outward-inclined shoulder configuration reduces the tip leakage flow rate, leading to a decrease in total pressure loss and an improvement in turbine aerodynamic efficiency. The efficiency enhancement exhibits a positive correlation with the outward inclination amplitude, reaching a 0.15% efficiency gain observed at an inclination angle of 30°, while the average heat transfer coefficient at the blade tip increases by 0.58%. Thickened outward-inclined shoulders maintain aerodynamic performance without compromise while reducing the heat transfer coefficient at the cavity bottom by 11.06%. Conversely, the inward-inclined shoulder configurations cause a significant increase in leakage flow, resulting in a maximum turbine efficiency reduction of 0.29%, while the overall blade tip heat transfer coefficient decreases by 3.83%. Thickened inward-inclined shoulders effectively suppress further leakage flow increase and achieve a 12.81% reduction in the cavity bottom heat transfer coefficient.