Ideally you should update your own site, you know a lot more about your business than anyone else. Even the most conscientious designer or marketer won’t have the same knowledge of your industry as you have. They won’t use the same words and phrasing as your customers. Sometimes that’s a good thing giving a new perspective but if your audience are experts on something they will appreciate your expertise.
An ornithologist will know that bird watchers like the term ‘birders’ but don’t like ‘twitchers’ just small mistakes like that can really turn people off.
Once was on the panel for a pitch where the pitcher kept referring to the area by the wrong name. Only slightly wrong but we knew we were not in that area so it became a distraction from what she was saying.
Sometimes its like journalists, when they write about an area that you know and they get that wrong, you lose faith in what they write about subjects you know nothing about.
Let your web developer build the site let them do the CSS, HTML, Design, Coding that is what they are good at. You are an expert on your subject/business sector, that is what your good at. With a modern content management system your web developer is just enabling you to get your expertise across.