We report a measurement of the B0 and B+ meson decays to the Ds-KS0π+ and Ds-K+K+ final states, respectively, using 657×106BB¯ pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. Using the Ds-→ϕπ-, K*(892)0K- and KS0K- decay modes for the Ds reconstruction, we measure the following branching fractions: B(B0→Ds-KS0π+)=[0.47±0.06(stat)±0.05(syst)]×10-4 and B(B+→Ds-K+K+)=[0.93±0.22(stat)±0.10(syst)]×10-5. We find the ratio of the branching fraction of B+→Ds-K+K+ to that of the analogous Cabibbo-favored B+→Ds-K+π+ decay to be RB=0.054±0.013(stat)±0.006(syst), which is consistent with the naive factorization model. We also observe a deviation of the DsK invariant-mass distribution from the three-body phase-space model for both studied decays.