The recently proposed symmetry-conserving energy density functional approach [G. Hupin, D. Lacroix, and M. Bender, Phys. Rev. C 84, 014309 (2011)] is applied to perform variation after projection onto the good particle number using the Skyrme interaction, including density-dependent terms. We propose a simplification to reduce the numerical effort to perform the variation. We present a systematic study of the Kr and Sn isotopic chains. This approach leads to nonzero pairing in magic nuclei and a global enhancement of the pairing gap compared to the original theory, which breaks particle number symmetry.