We're an ecommerce company who have been dealing with the baggage of "1-click buy" that we implemented a year back. To persist the cards we had to build our own

We're an ecommerce company who have been dealing with the baggage of "1-click buy" that we implemented a year back. To persist the cards we had to build our own infrastructure thereby increasing our PCI exposure. The yearly audits, honestly, are costing us a fortune. I need to make a business case around getting rid of the card related infrastructure and using some third party that provides tokenization-as-a-service. Are there any vendors out there who do that? After doing this,will my PCI exposure reduce significantly? As long as my customers are entering their CC details over the vendor's secure page and I'm making encrypted API calls to their service on HTTPS pages (like Stripe) do I still need to get PCI Certified?