How to state Curry's Paradox in propositional logic?

No, this is not Curry's paradox. (I'm sure you're familiar with what I write below; I'm including it for completeness and the benefit of other readers.)

Curry's paradox is used to "prove" an arbitrary claim, assuming the "admissibility" of a certain kind of self-referential statement. Namely, given an arbitrary sentence $\varphi$, Curry examines the sentence $$(*)_\varphi\quad\mbox{If this statement is true, then $\varphi$}.$$ This has the form "$A\implies\varphi$," and in order for it to be false $A$ must be true. That much doesn't rely on self-reference.

However, where self-reference comes in is in the observation that this situation can't occur: $$\mbox{$(*)_\varphi$ is false $\implies$ the hypothesis of $(*)_\varphi$ is true $\iff$ $(*)_\varphi$ is true;}$$ so we get "$\neg(*)_\varphi\implies(*)_\varphi$," that is, $(*)_\varphi$ is true.

Now we simply apply modus ponens to get $\varphi$.

When cast as a theorem, Curry's paradox amounts to a limitation, in any nontrivial formal system, on either the kinds of self-reference expressible in that system or the extent to which the standard rules of logic hold for such self-referential sentences within that system.

As you observed, the sentence you write down is not paradoxical; it is missing the self-referentiality which is crucial to Curry's paradox. What it is is the observation that makes the Curry paradox "tick:" we apply it to the assumption that "This sentence implies $\varphi$" is expressible in our system. But it's wrong to say that this is Curry's paradox; rather, Curry's paradox relies on the validity of the principle. This is a worthwhile observation since in weak formal systems (e.g. I believe relevant logics) Curry's paradox can break down.