In this work the D(d,n)³He and ⁹Be(d,n)¹⁰B reactions have been studied in a low-energy regime as neutron sources for skin tumor treatment in the frame of accelerator-based BNCT (AB-BNCT). The total neutron production and the energy and angular distributions for each reaction at different bombarding energies and for the thick targets considered (TiD₂, Be) have been determined using the available data in the literature. From this information, a feasibility study has been performed by means of MCNP simulations. The thermal, epithermal and fast neutron fluxes and doses at skin tumor positions (loaded with 40 ppm ¹⁰B) which are located on a whole-body human phantom have been simulated for different D₂O moderator depths. The best-case performance shows that a high tumor control probability (TCP) of 99% corresponding to a weighted dose in tumor of 40 Gy can be reached at the tumor position keeping the weighted dose in healthy tissue below 12.5 Gy, by means of the ⁹Be(d,n)¹⁰B reaction at 1.1 MeV for a deuteron current of 20 mA and a 30 cm D₂O moderator in 52 min. The availability of low-energy neutrons in the ⁹Be(d,n)¹⁰B reaction from the population of excited levels between 5.1 to 5.2 MeV in ¹⁰B and the convenience of a thin beryllium target are discussed. As a complement concerning alternatives to the Li(metal) + p reaction, the neutron yield of refractory lithium compounds (LiH, Li₃N and Li₂O) were calculated and compared with a Li metal target.