Can I create a registration form that securely handles cc information and is integrated with Salesforce?

Of course you can, and all in a single form too.
Registration form
With FormTitan you can build any type of form you want, the options are endless: contact forms, feedback forms, polls, surveys, web-to-lead, inquiry forms, registration forms and more.  Using a simple Drag & Drop you can use over 40 field types to create your own custom form. 

Payments
If you want to allow payments in this form, then this can also be done by adding payment integration. This will allow you to collect payments online via a certified payment processor like PayPal, Stripe, Authorized.net, USAePAY, iDEAL, Tranzila etc. Read all about the payment integration.

Integration with Salesforce Leads and Contacts
By integrating this form with Salesforce you can have all the registration data "pushed" to the relevant objects in SF, in this case: leads and contacts. Further more - if there is a payment involved, you can also have the payment details pushed to SF along with the rest of the data from the form. Read all about the Salesforce push integration.
You can also watch this video about checking if the filler is a already a registered contact or lead in Salesforce.

The FormTitan Salesforce integration is powerful - it allows you to connect with any object in Salesforce, including custom objects. 
Since it is Bi directional, it can also enable you to "Get" data from Salesforce objects and populate form fields.