We demonstrate guiding of cold 85Rb atoms through a 100-micron-diameter hollow core dielectric waveguide using cylindrical hollow modes. We have transported atoms using blue-detuned light in the 1st order, azimuthally-polarized TE01 hollow mode, and the 2nd order hollow modes (HE31, EH11, and HE12), and compared these results with guidance in the red-detuned, fundamental HE11 mode. The blue-detuned hollow modes confine atoms to low intensity along the capillary axis, far from the walls. We determine scattering rates in the guides by directly measuring the effect of recoil on the atoms. We observe higher atom numbers guided using red-detuned light in the HE11 mode, but a 10-fold reduction in scattering rate using the 2nd order modes, which have an r4 radial intensity profile to lowest order. We show that the red-detuned guides can be used to load atoms into the blue-detuned modes when both high atom number and low perturbation are desired.