The light-matter coupling between electromagnetic modes guided by a semiconductor nanowire and excitonic states of molecules localized in its surrounding media is studied from both classical and quantum perspectives, with the aim of describing the strong-coupling regime. Weakly guided modes (bare photonic modes) are found through a classical analysis, identifying those lowest-order modes presenting large electromagnetic fields spreading outside the nanowire while preserving their robust guided behavior. Experimental fits of the dielectric permittivity of an organic dye that exhibits excitonic states are used for realistic scenarios. A quantum model properly confirms through an avoided mode crossing that the strong-coupling regime can be achieved for this configuration, leading to Rabi splitting values above 100 meV. In addition, it is shown that the coupling strength depends on the fraction of energy spread outside the nanowire, rather than on the mode field localization. These results open up a new avenue towards strong-coupling phenomenology involving propagating modes in nonabsorbing media.