This solution will add a bit of code to the Master Page where you can create a custom Master Page for this. There is a lot of commotion around creating custom Master Pages or even editing the default and the following blog explains a bit about this: http://blog.sharepointexperience.com/2015/01/to-brand-or-not-to-brand/ . I wasn’t able to hide this successfully using for example a script editor web part so please let me know if you can do this
Manual to hide Add as a new version checkbox
You can copy and paste the following bit of code to the Master Page above the </head> entry.
You can find the library GUID at the library settings page:
The next time you upload a document the upoad.aspx page will look like the below:
This checkbox is also hidden when you link to this document library using a web part. This does not prevent users from overwriting files but adds a extra layer of awareness. The checkbox is always checked and this script also unchecks it. The standard question pops-up when a user tries to add a document with the same name to the library.
The user can select ‘Replace it’ or ‘Don’t Upload’