I would consider at least 24 hours, but likely more. Even a week later. The main reason being is that you don't know what's going to happen or if you'll change your mind.
What if you do change your mind, but the internet cuts out? If you set it for 12 hours later, you'll be scrambling trying to rescind the email(s). That's a ton of pressure, something I would want to avoid.
If you're found and set it for 24+ hrs later, at least it'll give you some time to try to sign in and rescind it even if getting out of the hospital will be difficult. I know this sounds silly, to try to take back the email(s) despite your friend or family member finding you, but maybe there are things in the email that you don't want them to know about when you're still alive. Or, maybe you sent it to a ton of people, and only a select few know about your attempt so you don't want the rest to find out.