Let $X, Y$ be projective algebraic surfaces with isolated singularities. Suppose they are diffeomorphic to each other. Denote by $\phi$ the diffeomorphism from $X$ to $Y$. Then does there exists a blow up $X', Y'$ of $X, Y$, respectively such that there exists a diffeomorphism $\phi':X' \to Y'$ which commutes with $\phi$ (via the natural maps from $X'$, $Y'$ to $X$, $Y$ respectively arising from blow up)?

What happens if $dim X=dim Y >2$? What happens if we assume that $X, Y$ lie as fibers over closed points of a family parametrized by a quasi-projective variety $B$ which is simply connected under the analytic topology (the underlying field is always $\mathbb{C}$)?