When you build a WebPlayer release, Unity already provides you with a good boilerplate to work with.
Take a look in the HTML and you will notice a section where it detects that no web player is installed. You can change this section as you need, including making it a direct download instead of a link to the Unity WebPlayer download page.
You should note however, that the Unity WebPlayer download page provides information and download for different operating systems, so if you roll your own download button, you will either have to implement such OS checks, or skip it and provide a degraded/incompatible experience for your users.
Finally, I can suggest you consider simply adding target="_blank" to the download link, so it will open in a new window. This will give you both the benefit of using Unity’s optimized download page, and the users still have your page open.