I am Norwegian, so with subject to "rense" and "vaske" means the same in Norwegian and Danish: Is "wash" to be translated to "rense". To me it means "vaske". However one doesn't "vaske" leather, one "renser". So in this case "rense" is a better word. Is perhaps the English word "wash" broader than "vaske" in Danish/Norwegian". Can it mean both "vaske" and "rense".
^^^Generally speaking at vaske (in Danish) is to wash, at rense (in Danish) is to dry clean. (A “false friend” is to rinse which is at skylle in Danish).
I suspect that the English version in the OP is a translation from Italian in which lavare (a secco) is to dry clean and lavare is to wash in a broader sense. My comment above was in reference to the Danish translation suggested in the second post. As you point out, leather is usually dry cleaned and not washed.