Hi Rebecca and welcome to the forum,
Customs are the ones who impose and collect any applicable import duties, so if a product comes into the country owing any duties, it doesn't get past Customs until they are paid. As you have identified, it's the buyer that is subject to the applicable duties, not you as the seller. As far as Customs are concerned in regards to any applicable import duties, as a drop-shipper, you play no role at all. They see it as a transaction between the sender and the receiver only.
Supplier's can't list import duties on their products because every country has different import duty thresholds, so in some cases a product can be sent to one country with no import duty applied by Customs, where it may incur that duty in another country. So suppliers aren't in a position to be able to calculate any duties on their products, that responsibility falls to the drop-shipper to ensure that their buyer is informed.
Now I keep using the term "applicable import duties" and I do that because of thresholds. Not everything that is imported is subject to any import duty. In fact most drop-shipped items come into countries well under any import duty thresholds, so it's not an issue at all. What you need to do is clarify the import duty duty and any restrictions that may impact on products you intend to sell with what ever country/s you intend on marketing in.
Then you should clearly identify any issues that may occur for interested buyers before they make the purchase so they can be forewarned, If there is no issues, then you have nothing to warn any perspective buyer about :)