The old man said that there are two parallel currents in the strait at different depths, flowing opposite to each other?
Even if you could dive to 450m I don't think the strait is deep enough. As a hint, most of the patrols travel from coast to coast (perpendicular to your path) with the occasional DD zig-zagging through the strait. Lots of smaller boats in those patrols too (and all the merchant traffic will keep your sonar busy).
My advice would be the same as Von Manteuffel's because that's how I crossed the strait. In your case, the schnorkell should make things much easier.