Unless you are VERY close to cashflow positive, don't do it! And if you are very close to cashflow positive, definitely don't do it!
Giving equity to a dev shop is a bad idea. Equity doesn't pay salaries, so they will put all paid work in front of your project, regardless of what they say or commit to.
There is an allusion of alignment (they are equity partners, so they care, right?), but it still doesn't pay salaries. So they will meet their commitment as slow as possible with the minimum of effort. That means it will take longer and be a lesser quality product.
You also don't need a CTO. A CTO is somebody who can build and manage a team of developers.
You need one senior full-stack developer that can build what you have in your head as fast as possible. It has to be only one person (read Mythical Man Month) and they have to be be senior level (or they will be slow because they won't know what features to cut out).
The easiest way to get a senior developer at a reasonable compensation level is to show them traction. So don't start the conversation until you have something tangible they can use to judge whether you're the real deal.
Just my two cents as a full-stack developer and a former CTO of a web dev company that did equity deals with clients. :)