Sounds like a good use case for Zapier -- you can create a trigger from Stripe to add a new customer to a list ("customers") who get put into an automation, where the first email contains the merge fields with stripe information.
New Customer - Triggers when a new customer is added.
New Plan - Triggers when you add a new Stripe plan.
New Charge - Triggers when someone's credit card is charged.
New Coupon - Triggers when you add a new Stripe coupon.
New Order - Triggers when a new order is created.
New Event - Triggers when a new event is added.
New Invoice Item - Triggers when a new invoice item is listed.