Your example has a hidden premise, and finding it is the whole exercise.
"This causes suffering, therefore it is wrong" is not valid as it stands. It becomes valid once you add "causing suffering is wrong", and that added line is not a fact about the world. It is a moral claim.
Hume's observation is that arguments of this shape always need such a line, and that writers slide it in without noticing. The conclusion contains something the premises did not.
This does not make facts irrelevant to ethics. It means facts do the work only once a value is already in play. Show that a policy causes suffering and you have settled a great deal, for anyone who already holds that suffering matters.