The fans Dell uses are actually pretty good, ball bearing, brushless. They are off-the-shelf products, with the exception that the connector is Dell-specific.
The compact design of the C models makes cooling very difficult without the main fan running. I wouldn't use it that way if I could help it. If you must, open the case and direct the external fan inside.
Aftermarketers do sell Dell-compatible fans, but make sure the site specifies the exact model it is to go in, as the fan features and connectors are model-specific.
Removing the heatsink to replace the fan, it is strongly preferable to remove all the old heatsink compound from both surfaces and replace it with new upon reassembly.