This app does just that. It doesn't disable Google Search, it just takes place of the swipe intent, so (i think) it's perfect for what you want! No root or anything required!
Re: Is there any way to disable Google Now on the Home button?
I know it's a little late, but... You want to disable only the swipe, but keep all of the other great functionality of the Google search app? Check this out. It does exactly that. It doesn't disable Google Search, it just takes...
Can't we just use encrypted everything from the connected device, or does the website have to support it? If so, maybe that's why they're blocking https?