Embed Shopify Checkout Widget inside Wordpress website

My WordPress limousine site already performs well, but the Wine Tour page suffers from Rezdy’s clunky functionality. I want to keep every other part of the site exactly as it is and simply swap the current booking widget for a clean Shopify checkout experience.

Here is the flow I have in mind:
• Each tour date will live in Shopify as its own product; stock levels will mirror the number of seats in the vehicle.
• A booking-button or custom JS SDK embed should appear in place of the existing Rezdy section on the WordPress Wine Tour page. Customers must be able to select their date, pay, and receive confirmation without ever leaving my domain.
• Design should inherit my site’s styling so the transition feels native.
• All back-end reporting must remain in Shopify, with the option to issue refunds or edit orders there.

Acceptance criteria
1. Embedded checkout loads quickly on desktop and mobile, no redirects.
2. Seat inventory decrements correctly after each purchase.
3. Order confirmation emails fire from Shopify using my branding.
4. Clear hand-off document: how to create new tour products and update embed code.

I’m open to any Shopify theme or plugin recommendations that make this smoother, as long as they do not require a wholesale rebuild of the site.

Please send a detailed project proposal outlining your approach, timeline, and any similar integrations you’ve completed.

The existing page should you wish to see is here https://www.thelimocompany.com.au/services/wine-with-a-new-friend/ Thats the event.