You have a few options...
First, you can carefully plan your shared templates. For instance, if you only need your templates in your HomeController, you can simply put DisplayTemplates in your ~/Views/Home folder.
Another option is to mark fields you want to use a different template. This can be done with [UIHint()] data attributes, or you can specify template name in the Editor/DisplayFor methods.
A different option would be to use not target your template at a generic type, such as DateTime, and make this a specific DataType. Then you can simply use it wherever you want it, and default to standard behavior otherwise.
If you want to use default processor when you have a generic template defined, there is no way that I know of to say "use the default template". Otherwise, you just don't use EditorFor/DisplayFor, and use TextBoxFor or similar instead.