We study non-adiabatic corrections to multibaryon systems within the bound state approach to the SU(3) Skyrme model. We use approximate ansatze for the static background fields based on rational maps which have the same symmetries of the exact solutions. To determine the explicit form of the collective Hamiltonians and wave functions we only make use of these symmetries. Thus, the expressions obtained are also valid in the exact case. On the other hand, the inertia parameters and hyperfine splitting constants we calculate do depend on the detailed form of the ansatze and are, therefore, approximate. Using these values we compute the low lying spectra of multibaryons with B < ~9 and strangeness 0, -1 and -B. Finally, we show that the non-adiabatic corrections do not affect the stability of the tetralambda and heptalambda found in a previous work.