I personally wouldn't expect a CTO to spend too much of their own time on building a website. Usually the CTO works more in a strategic capacity, ensuring the company is spending time on things that matter and that projects are on track.
If the website-project does have a very high impact on the business and you're fine with taking this type of position, then you should emphasize the value that you bring. A well-done, on-time project can be very valuable, especially if the business depends on the website a lot and there are competitors with better sites. Your experience can be invaluable and you should be rewarded for it.
If the company doesn't particularly care about the site, nor technology in general - which is the feeling I get from your description - then you might just not have much leverage.
Most importantly, do not make yourself look desperate. State what you want and then negotiate.