Unamplified 50-fs Ti:sapphire laser pulses are used to demonstrate physically different scenarios of non-linear-optical spectral transformations in the normal and anomalous dispersion regions in microchannel waveguides off the central core in photonic-crystal fibers. Signatures of polarization-dependent soliton self-frequency shift and dispersive-wave emission are shown to dominate the spectra of radiation transmitted through these waveguides in the regime where the pump wavelength initially falls within the range of normal dispersion, but lies close to the point of zero group-velocity dispersion. Form birefringence of microchannel waveguides allows polarization frequency switching of visible-range spectral components and results in a polarization sensitivity of supercontinuum generation. In the regime of anomalous dispersion, self-phase-modulation-induced phase matching is shown to result in modulation-instability-type four-wave mixing, leading to efficient generation of spectral sidebands at a typical interval of about 50 THz from the central frequency of the pump field.