A search for ηc(2S)→ppˉK+K−, together with measurement of branching fractions of χcJ(J=0,1,2)→ppˉK+K− in the ψ(3686)→γηc(2S) and the ψ(3686)→γχcJ radiative decays, is performed with (2712.4±14.3)×106ψ(3686) events collected with the BESIII detector at the BEPCII collider. An evidence for ηc(2S)→ppˉK+K− is found, with a significance of 3.3σ. The product branching fraction of B[ψ(3686)→γηc(2S)]⋅B[ηc(2S)→ppˉK+K−] is determined to be (1.98±0.41stat.±0.99syst.)×10−7. The product branching fractions of B[ψ(3686)→γχcJ]⋅B[χcJ→ppˉK+K−] are measured to be (2.49±0.03stat.±0.15syst.)×10−5, (1.83±0.02stat.±0.11syst.)×10−5, and (2.43±0.02stat.±0.15syst.)×10−5, for J=0,1, and 2, respectively.