How can I pass the cost of SaaS on to my customers?

We are a software consulting agency and order various SaaS solutions on behalf of our customers. At the moment we pay these services with our company credit card and invoice the customer.

This is cumbersome and time intense.

One opportunity would be to query all possible accounts via the API and create an invoice (Lot of Coding). Another possibility would be to allocate each customer a dedicated credit card and simply pass on the costs.

Is there such a SaaS service or a provider that issues virtual credit cards like "Stripe Issuing"?

We are in Europe (Switzerland) so Stripe Issuing isn't currently available to us.

thx