One of Delta feature is to have ACID transaction when you commit your file so what you are asking goes against this.
If you really want to do this I would recommend having your data partitionned by customer_id so that when you need to erase from history a specific client you just have to dump a specific partition.
This would involve in 2 counter parts :
you will experience slower requests if you have very few rows per customer_id and yet a large number of them
your request have to always filter on customer_id (because you've just broken the mecanic of Delta erasing a file that is still existing from his point of view)