re: "Is it possible to migrate the existing MySql database and replace Cakephp with Opencart?"
Yes.
re: "So we could save all the time we invested to create the custom database and use it with the Opencart platfrom?"
Yes.
re: "How long should an operation like this take?"
It depends on who is doing the work, as well as the particulars of your current system and what precisely it is that you want to end up with.
re: "Is it possible?"
Yes, definitely.
re: "What could be the price range to achieve it?"
It depends on who you have do the work, and the precise nature what you have now, as well as what it is that you want to end up with.
As helpful as we like to be, here in the Community Forum, there may not be much more we can do for you here. The place to get more accurate information, be able to talk to specialized developers with expertise using these technologies, and get bids and quotes is in the main site:
http://www.upwork.com
Your best bet would be to place a job posting to hire people to CONSULT with you about this, without actually doing the work. Then hire 5 or 6 people, and talk with them for twenty to thirty minutes. This will help you decide exactly what you want to do, and who to hire to actually do the work.
Keep in mind that in migrating from CakePHP to Opencart, you're talking about "migrating" from a general PHP framework to a turnkey shopping cart solution. These aren't the same class of technologies.
Some sites use CakePHP and Opencart simultaneously, although for most sites, this is unnecessary. It sounds like what you want is a CakePHP-free site which uses Opencart and other than that just uses a generic PHP backend. That's a good call. But again, whether or not this is best for your overall system (getting rid of CakePHP completely or using it along with Opencart) would depend on your goals and plans.