We experimentally compared for the first time, two techniques of optical fiber preform shaping based on the mechanical grinding and thermal CO2 laser processing from the point of the inner-cladding losses. The shaped preforms were fabricated of coreless pure silica technical rods as well as high purity silica Heraeus F300 rods and drawn them into coreless multimode fibers with various inner-cladding geometries coated with a low index fluorinated polymers. The background losses of the fibers were measured via the cut-back method and compared to the losses of the unshaped fibers with a circular cross-section. Results show that both preform-shaping techniques would induce additional losses in the inner-cladding. High surface scattering losses were observed in the mechanically-grinded fibers. On the other hand, the mechanical grinding retains the advantage of a significant reduction of attenuation peaks attributed to OH-groups that penetrated into the preform surface during the preform collapse. On the contrary, CO2 laser thermal-shaping provides the advantage of quick, fully automated shaping with smooth surface finish and induces much lower scattering losses, but it is not so effective in removing water penetrated surface layer of the preform so that OH-groups diffuse deeper towards the preform center. Additionally, laser thermal-shaping allows processing the preform to complex shapes which are more effective in scrambling cladding modes. Some of the absorption peaks of OH-groups and fluorinated polymers may be rather close to common pumping wavelengths and this should be considered in the design of the double-clad fibers and selection of proper shaping technology.