Hello there,
I'm a linux system administrator at a web hosting company. I've dealt with thousand of issues like this.
I would like to say if site is consuming high CPU load, why are you going for a developer to optimize code? I don't think if optimization will help that much.
I think, you need a server admin to check the server first. Sometimes, it doesn't depend on optimization really, you might have to upgrade server too but all depends after checking the server.
Also whats the traffic to your site? is it hosted on a shared hosting, VPS or dedicated?
Please message me for further details.
Thanks.