Any-to-any singing voice conversion (SVC) is confronted with the challenge of ``timbre leakage'' issue caused by inadequate disentanglement between the content and the speaker timbre. To address this issue, this study introduces NeuCoSVC, a novel neural concatenative SVC framework. It consists of a self-supervised learning (SSL) representation extractor, a neural harmonic signal generator, and a waveform synthesizer. The SSL extractor condenses audio into fixed-dimensional SSL features, while the harmonic signal generator leverages linear time-varying filters to produce both raw and filtered harmonic signals for pitch information. The synthesizer reconstructs waveforms using SSL features, harmonic signals, and loudness information. During inference, voice conversion is performed by substituting source SSL features with their nearest counterparts from a matching pool which comprises SSL features extracted from the reference audio, while preserving raw harmonic signals and loudness from the source audio. By directly utilizing SSL features from the reference audio, the proposed framework effectively resolves the ``timbre leakage" issue caused by previous disentanglement-based approaches. Experimental results demonstrate that the proposed NeuCoSVC system outperforms the disentanglement-based speaker embedding approach in one-shot SVC across intra-language, cross-language, and cross-domain evaluations.