In-situ mini-invasive maintenance is crucial for the safety insurance and economic purpose of aero-engines. Cable-driven continuum robots (CDCRs) with excellent flexibility and accessibility in unstructured and highly restricted spaces show unique strength and potential for in-situ mini-invasive aero-engine maintenance. This paper addresses limited load capacity, torsion problem, and low morphology accuracy of CDCR for in-situ mini-invasive maintenance of aero-engines. First and foremost, a novel contact-aided compliant mechanism (CACM) by embedding micro-bearings is proposed to enhance the torsional resistance of CDCR and reduce joint friction. Then, a comprehensive kinetostatic modeling framework for CDCR is derived, focusing on time-varying friction modeling to improve morphology accuracy. Comparative experiments indicate that the proposed CACM-based CDCR outperforms the conventional twin-pivot CDCR at least 24 times in terms of torsion stiffness, stiffness enhancement (interlock configurations) of more than 100 times, and the morphology error of our model is less than 2.5%, which demonstrates the effectiveness of the proposed design and modeling method.