Hi GK Safety,
Either option a) integrating a blog into your current site and b) starting with WordPress. It is arguable which one will take longer as they both have so many variables involved.
Do your customers feel that your current website is lacking? Have you spoke to any of them to ask?
If you already have established search engine rankings for a number of pages on your existing site, you don't want to loose these so this part has to handled carefully if you decide to update the site using WordPress.
If selecting a pre-made template then Wordpress can be very easy to use and will not necessarily take more time then integrating a blog into your current site. However finding a template you like can take a considerable amount of time and then you have to do a little research to understand why one template (with its' implemented features) is better (functionally) than another.
If you have any unique functionality on your existing site then it is unlikely to get that unique functionality working 'out of the box' in WordPress.
IMHO WordPress has a cludgy way of handling extending the PHP landscape, so If you like using OOP with PHP pretty much throw that logic away.
If you switch to WordPress it will make it easier overtime to refresh you site's look but keep the existing content.
To the positive WordPress has excellent documentation, so if you need to learn something you can not only find a gazillion articles on the Web but also good information from WordPress too.