Diffeomorphism between a subset of $\mathbb{R}^2$ and the annulus

Question

Suppose $\gamma_1, \gamma_2:I\to \mathbb{R}^2$ are two simple closed and smooth curves. Suppose also that the images $\gamma_1(I)$ and $\gamma_2(I)$ are disjoint and $\gamma_1(I)=S^1$. Is it true that there exists a $C^\infty$-diffeomorphism $\Phi:\mathbb{R}^2\to \mathbb{R}^2$ such that $\Phi(\gamma_1(I))=S^1$ and $\Phi(\gamma_2(I))=\{x\in \mathbb{R}^2 \big|\ \|x\|=2\}$ ?