In this paper, we follow recent developments in non-parametric learning and show how LLMs can be efficiently fine-tuned to achieve strong few-shot performance on WSD for historical languages. We test our hypothesis using (i) a large, general evaluation set taken from large lexical databases, and (ii) a small real-world scenario involving an ad-hoc WSD task. Moreover, this paper marks the release of GysBERT, a LLM for historical Dutch (1500-1950).