We have introduced the Skeleton Cyclotron, a high-temperature superconducting (HTS) air-core compact cyclotron designed to produce medical radioisotopes (RIs) to be used in targeted alpha-particle therapy, an innovative approach to cancer treatment. The coil system of the Skeleton Cyclotron comprises circular main coils for creating an isochronous field and non-circular sector coils to generate an azimuthally varying field. All of these coils are wound using the REBCO tape with a no-insulation (NI) winding technique, chosen for its ability to provide high current densities and thermal stability. To demonstrate the feasibility of our concept, we developed a half-size prototype called the Ultra-Baby Cyclotron. This prototype includes three pairs of sector coils and four main split coils. To enhance the durability of the coils and protect them from the intense electromagnetic forces involved, we reinforced them with a YOROI-coil (Y-based Oxide superconductor and Reinforcing Outer Integrated coil) structure. In the summer of 2022, we started testing on the Ultra-Baby Cyclotron, and then we conducted measurements of mechanical deformations in the coils. Additionally, we conducted numerical simulations. This study presents the experimental and numerical results regarding the mechanical behaviors of NI-REBCO coils in the Ultra-Baby Cyclotron.