That implies that your search box is actually being provided by a delegate control. This is a good thing - it means you don't need to change your master page.
Instead, you need to create a new Feature which contains a delegate control. This is a reasonable description. It's for 2007, but 2010 isn't very different.
When active, your Feature's delegated control is put into the 'DelegateControl' on your page. Now, what control do you want to place in?
Well, the Small Search box is actually provided in a few different forms by different Features. This article describes creating the control for a new one. Again, it's 2007, but 2010 is pretty much the same. Also, this is a good example.
Note that you will need a lower Sequence attribute than the existing search box.
So, in short, you can do all of this without deploying a new control - rather, you're using the existing ones. You do have to create a new Feature, but you only have to write XML. There's no C# involved.
Regarding getting a particular scope - I would acheive this creating a search center within my site collection, and then on the core results web part setting the scope that I want to apply to the results shown. There's an example of this here. Alternatively, you could append the scope to the search query.