Representations of $\mathbb Z^2$ in ${\rm Symp}(S^2)$

Question

Suppose $f_1$ and $f_2$ are two commuting symplectomorphisms of the sphere $\mathbb S^2$, of orders different from $2$. Is it possible to deform the pair $(f_1,f_2)$ to the pair of identity maps via a continuous family of pairs of commuting symplectomorphisms?