We study the influence of structural lattice fluctuations on the elastic electron transport in single-wall carbon nanotubes within a density-functional-based scheme. Results obtained from a frozen-phonon approach as well as from molecular dynamics simulations are compared. The linear conductance can be calculated after appropriate configurational averages. We demonstrate that the effect of structural fluctuations can be captured by the Anderson model of disorder. Further, the influence of individual vibrational modes on the electronic transport is discussed and it is shown that at different energies the normal modes hierarchically contribute to the charge transport process.