Is it possible to delete an external ID?

I am trying to remove an external ID after an order is cancelled so it can be used again.

"Revise an Order by Customer and Order ID" will let me change the number, but it won't let me delete it.

I have tried sending:

{
"external_id":""
}

and

{
"external_id":null
}

Both go through but don't change anything.