There doesn’t appear to be an user-friendly way to participate in a transparent coinholder poll. In previous transparent polls (before a shielded coinholder voting mechanism existed) users would transfer ZEC from a shielded address or another transparent address into a transparent address using Zecwallet Lite. They would then include their vote in the memo field of a small transaction sent to the poll address. It was a rather straightforward process. However, now that shielded voting exists, that process is no longer relevant since you can now vote using your Orchard notes. Transparent-only wallets like Trust Wallet don’t support the memo field, so they can’t be used for this kind of poll.
Given those constraints, the best path forward seems to be the process outlined by @outgoing.doze below, which involves signing a transaction. In addition to what he outlines, it will also be necessary to check the signature. Also, we should consider how to implement this in a way that avoids unnecessary deanonymization of wallets.