I would not leave the official will at the scene. Not a good idea. That's a very important piece of paper. A copy of it is OK. I do think sending a delayed message to your executors is a good idea about where they can find your will. If you're concerned about them getting the messages, be redundant and setup multiple email accounts with delayed send features and send multiple messages to them that way. I'm not sure if text messages have a delayed send feature. Maybe there is an app for that? You can also have a note in the apartment telling them where your will is. Leave a note with yourself telling the police who to contact. Also, depending on where you live, sometimes your will can be filed directly with the court. Nothing suspicious about that. That's what I did. Your official will should be kept in a strongbox at your home, or in a bank's safety deposit box, along with any further instructions you would like to leave.
Also, make sure your friends, family, your "executors" are familiar with your "new" email addresses before you go, so the messages don't end up in spam, or simply get deleted. Nothing suspicious about creating new email addresses. People do it all the time.