IE as you know it is a Windows app that wraps the internal browser engine. The internal engine isn't going anywhere as many apps rely on it. Just IE, the application, is going away. Therefore if you rely on MSHTML then you should be fine. In fact the IE Mode that Edge supports to eliminate the need for having IE installed is using this very engine as well.
Having said that though it is not completely clear what all functionality
ShDocvw you are relying on such that it should continue to work. You should probably go ahead and test your app on a machine without IE installed to ensure it works correctly. For cases where it triggers the browser then now you would expect it to load Edge instead. If a web app doesn't work in Edge then that is where IE mode comes in.
I should also point out that MS has mentioned in their FAQ that some COM scenarios were broken with this change. You should ensure you are testing against a pre/post-patched system.