Increasing attention is being dedicated by the NLP community to gender-fair practices, including emerging forms of non-binary language. Given the shift to the prompting paradigm for multiple tasks, direct comparisons between prompted and fine-tuned models in this context are lacking. We aim to fill this gap by comparing prompt engineering and fine-tuning techniques for gender-fair rewriting in Italian. We do so by framing a rewriting task where Italian gender-marked translations from English gender-ambiguous sentences are adapted into a gender-neutral alternative using direct non-binary language. We augment existing datasets with gender-neutral translations and conduct experiments to determine the best architecture and approach to complete such task, by fine-tuning and prompting seq2seq encoder-decoder and autoregressive decoder-only models. We show that smaller seq2seq models can reach good performance when fine-tuned, even with relatively little data; when it comes to prompts, including task demonstrations is crucial, and we find that chat-tuned models reach the best results in a few-shot setting. We achieve promising results, especially in contexts of limited data and resources.