For it to look professional make a small setup program.
You currently have sql scripts that you use to create your db.
Make yourself a small xml file that contains the path to your scripts.
Create a small c# library that will connect to the db server, and run those scripts.
You can test this outside of the setup, in visual studio, then add it to the setup like this.
To do this from your setup all you have to do is put the xml file in a component so it is deployed,
And create a custom action in your setup, that will call your C# lib, read the xml and run the scripts on the sql server to create your db.
Also, from a setup program it's easy to set a registry key to identify the version of the your db that you just installed.
The minuses and pluses: It's a bit of work to start with, but with this you'll have all the ground work done to handle upgrades automatically later on, to do so, just add an upgradeScript section to your xml, an attribute called version for each upgrade script, and simply compare it against the version of the db you have save in the registry. The advantage is this way it can easily scale with your project.