@DRMasterChief What you want to implement in your store doesn’t require any changes to Thirtybees or any additional modules.
You want a button that links to a contact form where the customer must submit a request to cancel their order. Just add a link or button anywhere in your store that leads to the standard contact form, and that’s it.
And since this solution has nothing to do with the functionality of the "Cancel order" button, has no integration with the store, and doesn’t automate any actions in the store (such as automatically changing the order status), that’s a different matter. What you’re proposing is just plain old email writing. The customer has to write an email providing all their details, then the store staff has to read that email and take some further action on the order.
And this whole "canceling orders without logging into the customer’s account" thing is total nonsense. Hackers will be canceling all the orders in the store every day. There are no safety measures in this solution.
Here’s an example of how it’s done in WooCommerce: https://woocommerce.com/products/customer-order-cancellation-for-woocommerce/
The customer logs into their account, sees a list of their orders, and on that list there’s a "Cancel order" button—they don’t have to spend an hour filling out confusing forms where they have to provide all their personal information.
In my module, I implemented this as follows: the "Cancel order" button is always visible in the store's navigation bar; when the customer clicks it, they are taken to their order list and can cancel the order with a single click. In the module’s configuration, you can exclude order cancellations for virtual products and customer personalized products; by law, such products are non-returnable. When the customer clicks the "Cancel order" button, the order status is automatically changed to "Order canceled". Many electronic payment gateways offer automatic refunds when the status is changed to the one specified in their configuration—in this case, we achieve 100% automation of store operations that require no action from store staff.