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Given the recent interest in magnetohydrodynamic (MHD) waves in pores and sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by modeling solar photospheric waveguides with a cylindrical inhomogeneity comprising a uniform interior, a uniform exterior, and a continuous transition layer (TL) in between. Performing an eigen-mode analysis in linear, resistive, gravity-free MHD, our approach is idealized in that, among other things, our equilibrium is structured only in the radial direction. We can nonetheless address two damping mechanisms simultaneously, one being the Ohmic resistivity, and the other being the resonant absorption of SSKMs in the cusp and Alfv$\acute{\rm e}$n continua. We find that the relative importance of the two mechanisms depends sensitively on the magnetic Reynolds number ($R_{\rm m}$). Resonant absorption is the sole damping mechanism for realistically large values of $R_{\rm m}$, and the cusp resonance in general dominates the Alfv$\acute{\rm e}$n one unless the axial wavenumbers are at the lower end of the observationally relevant range. We also find that the thin-boundary approximation holds only when the TL-width-to-radius ratios are much smaller than nominally expected. The Ohmic resistivity is far more important for realistically small $R_{\rm m}$. Even in this case, SSKMs are only marginally damped, with damping-time-to-period-ratios reaching $\sim 10$ in the parameter range we examine.