This would require some custom Java code at the moment.
For the Advanced Search you will need to modify org.alfresco.web.ui.repo.component.UISearchCustomProperties.generateControl().
For the property sheet you'll need to change org.alfresco.web.bean.generator.DatePickerGenerator, or better still override the DataPickerGenerator with your own using the component generator framework, see http://wiki.alfresco.com/wiki/Component_Generator_Framework for more details.
I will add this as something to make configurable for a future release.