There are various options available to you depending on how much you want to traumatize your character:

— MAN OVERBOARD: The average seawater temp is 13.6°C / 56.5°F. Without magical assistance, you will begin to lose dexterity after 10-15 minutes in the water; you will lose consciousness after 1-2 hours, and will die of hypothermia after 1-6 hours if you didn't already drown after passing out prior to that. Accordingly, if you want your character to go overboard and survive, you have to be pulled into a lifeboat or use a lot of magic to help you last until Alfred can get down there to rescue you. The Voyager will be onsite about 20 hours after the wreck. On the upside, you don't have to worry about sharks? Assuming you survive, you'll make the first survivor drop off (more on that in the next section).
— LIFEBOATS: Boats can hold about ~20 people, though may have fewer depending on the circumstances when they were launched. They are supposed to be stocked with some provisions, but feel free to adlib whether your lifeboat actually is or how well those provisions actually provide for your occupants. Lifeboat survivors can be found anytime between the 9th and the 16th, depending on how far you drift from the main shipwreck, and can accordingly make survivor drop off one, two, or be brought it after.
— CASTAWAY: With either of the above options, feel free to find yourself on a deserted isle! And by deserted isle, I mean a glorified rock surrounded by sea. You can happen upon this island at any point and may be rescued any time between the 9th and the 16th, depending on how far it is from the wreck and how good you are at signaling your position.
— GOING DOWN WITH THE SHIP: About half the ship will be lodged against the rocks in such a way that it doesn't get underwater, so if you're in that section you can just stay onboard and wait for rescue. If you are in an open/populated area, this will probably happen by midday on the 9th. If you're trapped in a room slowly filling up with water or something, you might not get found until the 10th. Either way, you make the first survivor drop-off.
— SOMETHING ELSE: Want to be picked up by Muggle fishermen? Have your bubble-head charm work so well you sink to the bottom and discover Atlantis? Wrestle a mermaid? Whatever you please. If you want my help determining what is reasonable given our shipwreck parameters, just holler and I'm happy to bandy about ideas

Don't want trauma, but have already established IC that they left with the cruise? Have them miss the boat in any port prior to Brest and they can stay safe and sound in port and return to England at their leisure.

News of the wreck may start as a ~rumor as early as April 9th and will probably be announced more officially on the 10th. The Voyager will have owls onboard but not enough for every survivor to get one to themselves, so letters to friends and family will be bundled and delivered to the Ministry of Magic atrium, where they can then be sorted and distributed. This means you can have threads in the Ministry anxiously waiting for word of your loved ones if you're inclined (or Ministry officials can be frustrated with crowds milling around doing nothing but getting in the way). The first group of survivors will arrive in Portugal on April 10th, when they will have more reliable access to owls, and the Ministry can arrange transport home from there. The second group of survivors will get dropped off in Plymouth on April 12th where they will have access to floo. A few stragglers may be picked up here and there up until April 16th, at which point anyone who hasn't been recovered will be declared lost at sea.

Anyone participating in the rescue effort should be able to leave with minimal notice on the morning of April 9th and be underway until April 16th.

Mediwitches/healers are appreciated, as are Ministry officials who have "rescuing people" vaguely within their skillset (I'm unsure which department this really fits under, but if you can make it make sense, go for it). There might also be space for someone in a more administrative capacity — taking names and statements, investigating what happened to bring the ship down, making a list of who is missing, etc). Total onboard support staff should be pretty small because we want most of the space to be available for survivors, so please lmk if you plan to have your character onboard!

Mediwitches/healers and people to take statements and keep records would also be appreciated in Portugal in the 10th (plus Ministry folks to coordinate transport back home) and in Plymouth on the 12th.