Looking to see if a part time CTO or a CTO as a service type model would be a good option, looking for feedback about past experiences and potential gotchas to watch out for.
What I would suggest is that instead of focusing on a title, you instead make yourself a very specific list of the skills/tasks that need to be accomplished. You may not need a CTO at all.
Regardless of how you label the help, what's important is that you know what needs to be accomplished. Don't assume a CTO is magically the solution to a tech problem. You may accomplish your objectives with a collection of other resources than a single elite resource.
So I've considered offering this service. I can't answer your question since I would be the "for hire CTO". My peers who do this generally are sound engineers. "Consulting CTO" really is just a marketing term. What you really want is a 1099 (if you're US-based) principal engineer (someone who will own the full scope of consultation to implementation to quality assurance).
Think about this.. the CTO is looking to make an honest transaction of business and is going to not chew off your limbs in shares. They'll gracefully exit as your business model matures into more protracted enterprise engagements / compliance. Honestly, that de-risks a Series A.
If you want I can elaborate on my model. I'm a bit further along than gaining from a relationship as a principal alone.
The downside to Paul's mention is that you have to formulate the "requirements" which at-best you'll have an advisor you pay to draft documents for you. I've had my time wasted by people trying to put me in this position, so I don't think very positively about it.