You may consider hiring a contractor too. Less commitment on your part than giving away part of the biz. Especially if you just need some performance tuning.
We also think finding the right contractor is smart idea too because it will allow us to make the changes without equity like you said. Which than we can scale the product on our own to get the traction/funding we need to hire the right CTO.
We've really only had one investor question us on not having a CTO anyway.