To have the DateTimePicker show only the time, change the Format to Time.
I know of no way to get the DateTime picker to display a drop down with the time in it - it only shows the Calendar control (even if you specify the Format as Time).
The dropdown used in Outlook isn't using the DateTimePicker afaik. You can tell because the button to the right is a separate button, not part of the actual control. I would guess they're just looping and filling a Combobox (or something similar) with the time values they want.
As far as removing the drop-down button, the closest I can see is setting ShowUpDown to True, which changes the DropDown button to two of the tiniest up/down buttons I've ever seen.
If you're really pressed for space and want to remove the button to save 16 pixels (or whatever the width is), you *might* be able to remove the button using the API. But I would definitely NOT try that unless *absolutely* necessary. And I don't think you'll find much help on how to do it.
-Nerseus