All you can do is uncheck the IE option in Programs and Features/Windows Features. I would think that the default search provider could be different for each browser you use. (Don't know for sure since I only use IE.) However, I have set Google as the default search provider for IE which, once set, never changes nor do I see any request to change it. In IE go to Tools/Manage Add-ons/Search Providers; select the current default and if it's not what you want click "Find more..."; in the gallery type the name of the provider to the left of the magnifying glass icon; when you see the one you want add it. One added it can be highlighted in the Manage Add-ons window and made the default by clicking "set as default". Now you do not need to remove IE at all, just don't use it for browsing the web.