Hi Malcolm and welcome to the forum,
Blind Shipping technically means that the supplier may send your customer an invoice direct, but without their supplier details on it. Drop shipping technically means no invoice will be sent to your customer without any invoice at all, which is exactly what you really want when drop shipping. You really need to be the one who is doing the invoicing to your customer, not your supplier as the price that will be on their invoice will be your supply price, not your sale price that they have paid.
I would suggest you just clarify with the two suppliers their invoicing. Make sure the invoice comes to you, only the package itself goes to your customer. Then you can do your own invoicing and keep complete control. If any supplier insists on sending an invoice with the package itself, blind or not, stay clear would be my advice.