You can't have crop handles only without resize handles. However, you can use the Format Picture pane to get accurate crop. You'll notice from there that Microsoft put Crop and Resize options together too; apparently this was made on purpose so that crop and resize handles share places on pictures.
Note: Picture edit tools in Office are still limited to simple use, even after being developed so well. I'd recommend using external image editors for every need, regardless of being simple or not.