You say this is a company you could see yourself working at for some time, and have been handed C suite level responsibility that you can handle. So seemingly you are content and able to handle the work load.

Learning to be a IC is something anyone can do given time, but learning to be a manager can only be learned by being on the job, if you are able to get it in the first place.

Now is really not a good time to jump ship, unless you know for certain that the new position is going to be stable.

Grab the opportunity, do a good job and perhaps study how to be a better IC in your free time. You'll come out on the other side with skills and experiences that many in this field will be missing.