Do you think a CEO is important in doing a first raise?

My company is looking to do a moderate size raise, $300-500k immediately and $2-3M "eventually". My expectation is that it would be some combination of angel investment, VC investment, and strategic investment.

We're a chemical manufacturing startup, and don't have funding with which to pay a CEO an actual salary. We can demonstrate credibility and experience selling to our target customers without one, and have access to potential investors, but we haven't done a raise before.

One big worry is that the right CEO to help a company pre-funding do a first moderate sized raise is not the same CEO to take a company from a first raise to a second one or revenue. I'd also expect a VC firm to want to have a role in selecting the CEO, which seems like a recipe for trouble.