We study the influence of structural lattice fluctuations on the elastic electron transport in single-wall carbon nanotubes within a density-functional-based scheme. In the linear-response regime, the linear conductance is calculated via configurational averages over the distorted lattice. Results obtained from a frozen-phonon approach as well as from molecular-dynamics simulations are compared. We further suggest that the effect of structural fluctuations can be qualitatively captured by the Anderson model with bond disorder. The influence of individual vibrational modes on the electronic transport is discussed as well as the role of zero-point fluctuations.