In recent years, Fiber Bragg Grating (FBG) optical fibers have gained popularity to be used for shape sensing (SS) of continuum manipulators (CMs) developed for various minimally invasive surgeries. Despite their benefits, arduous and costly fabrication procedure together with the limited and discrete sensing nodes on each fiber are some of the main shortcomings of FBG-based SS of CMs. Aiming at addressing these challenges and leveraging the Optical Frequency Domain Reflectometry (OFDR) technology, I propose a design and evaluate the performance for a shape sensing assembly (SSA) that consists of solely one distributed fiber optic sensor and a flat Nitinol wire. The proposed SSA and fabrication procedure can collectively address the mentioned drawbacks of FBG-based SSAs (i) by continuously measuring the strain along the length of fiber at a high resolution, and (ii) offering a simple, cost-efficient, and repeatable manufacturing process that reduces the assembly time and improves accuracy. To evaluate performance, the SSA was subjected to three separate bending experiments. In free-bending, the SSA resulted in an average tip error of 0.657 mm and shape error of 0.549 mm. For S-bending, the average tip error and shape error are 1.840 mm and 0.846 mm, respectively. In obstacle bending, the SSA achieved an average tip error of 5.292 mm and average shape error of 2.711 mm.