It's like trying to secure your house from burglary. You can make it difficult or expensive for the crook to break in, but you can't guarantee that they won't be able to do so if they are willing to work at it hard enough.
But odds are very good that if your prospective client had the technical skill to break your protection, they wouldn't need your database solution in the first place.
Option 1: Use FileMaker Advanced to create a run time copy of your solution. Lock of your account with an account name/password/privilegeSet that only permits them to do what they need to evaluate your file. Use FileMaker Advanced to remove the admin account from this demo file. I would even remove all accounts except the limited access account I wanted them to use. Add a script that renders the file inoperative after a certain period of time. One way is to add a start up script that counts the number of times that the file has been opened and just uses Quit Application to close the file right back down if it has been opened that number of times. Add text to layouts that label them as "DEMO" in large red letters in a way that their password does not permit them to modify it.
Option 2: Host the database from a server and provide them with remote access to your hosted file with that same limited access account. This prevents them from having a physical copy of the DB so you don't have to lock it up so tightly, but it won't be as responsive to them as a copy on their computer.
Drop box vs. Email? As long as the files you attach are small enough not to create issues with your client's email service, it really makes no difference as either way, they get a physical copy of your files. The one advantage I can think of for Drop box is that if you share the directory to your evaluation copy, you can set up means within your database solution where the client can provide feedback on your solution in context of specific areas of your database. Then you would want access to the same file to see those comments and then the shared directory makes that very convenient.