If the executives don't get a timeline from you, they'll get it from someone less knowledgeable. Estimates made in ignorance are almost always underestimates because they omit critical work the estimator is unaware of. Therefore, this (bad) estimate will also be a "lowball" estimate, but it will be the only hard number executives have to make their decision. So they'll greenlight the rewrite and more than likely put the lowball estimator in charge. Being vocal, honest, and credible about estimates and the true cost of projects is always the best move.

The strategy is to be vocal, honest and credible by estimating features, not the whole rewrite. The rewrite happens by strangling the original application, feature by feature.