Vibrational spectroscopy is a powerful method for the label-free identification of molecules. Spontaneous Raman spectroscopy integrated with an ultra-thin fiber-based endoscope can provide remote, local, and minimally invasive chemical analysis in many fields from biomedical diagnostics to the materials industry. Miniaturization of the probe in combination with a large field of view (FOV) and high sensitivity would be beneficial for a broad class of applications. Here we quantitatively analyze signal-to-noise ratio (SNR) and the sensitivity improvement due to wavefront shaping. We show that wavefront shaping in an ultra-thin single-fiber probe allows to decrease the total measurements time up to several orders of magnitude even without any prior knowledge of the Raman particle location. Such a fiber probe is well suited for minimally-invasive endoscopy in biological and medical applications.