This is the most common practical problem Taiwan exporters face. Try these three layers in order; do not jump to the third layer immediately:
【Layer 1: Educate first】 Send an explanatory email clarifying three things: it is an EU regulation, you are not being unreasonable, and what specific information you need. Most suppliers are stuck at "I don't know what this is," not "I'm unwilling to cooperate."
【Layer 2: Help them fill it out】 Create a draft using a tool, fill in 80% with known data, send it to the supplier for confirmation and material details, have them sign and return. For small manufacturers, "you've already filled most of it, I just need to confirm and sign" is completely different from "you create an entire document yourself." This layer usually solves it.
【Layer 3: Turn it into a business decision】 When the first two layers don't work, you have only two options: change suppliers, or sign it yourself (but this means you are taking on uncontrollable risk: if the supplier changes materials, you won't know, and the Declaration becomes invalid immediately).
Key to reducing risk: establish a written change notification agreement with the supplier (they must proactively notify you of changes to materials, structure, or supply sources).