Pushing tasks performed by aerial manipulators can be used for contact-based industrial inspections. Underactuated aerial vehicles are widely employed in aerial manipulation due to their widespread availability and relatively low cost. Industrial infrastructures often consist of diverse oriented work surfaces. When interacting with such surfaces, the coupled gravity compensation and interaction force generation of underactuated aerial vehicles can present the potential challenge of near-saturation operations. The blind utilization of these platforms for such tasks can lead to instability and accidents, creating unsafe operating conditions and potentially damaging the platform. In order to ensure safe pushing on these surfaces while managing platform saturation, this work establishes a safety assessment process. This process involves the prediction of the saturation level of each actuator during pushing across variable surface orientations. Furthermore, the assessment results are used to plan and execute physical experiments, ensuring safe operations and preventing platform damage.