You can work with normal property without Dependency property if you create a Base class for your Page.
public class BaseWindow : Window
{
public string MyProperty { get; set; }
}
<local:BaseWindow x:Class="BaseWindowSample.Window1" x:Name="winImp"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:local="clr-namespace:BaseWindowSample"
MyProperty="myproperty value"
Title="Window1" Height="300" Width="300">
</local:BaseWindow>
And it works even though MyProperty is not a Dependency or Attached.