Use the System.Diagnostics.Process.Start method. I would simply do it in your script, but you can add that method to your Toolbox to add into an automation since it is static.

If you need to automate the website being launched with an adapter, then you'd either set the StartPage property of the adapter and start it with the URL, or you would need to navigate the browser control of the adapter. This option seems unlikely though since you are generating the URL from a script and its probably not a static one you would interrogate.