One important reason for updating a website that's years old might be to incorporate a more mobile-friendly design, since the sale of mobile devices are now outpacing desktops, and expected to outnumber people by the end of the year.
Since you're already obtaining good ranking results and your customer is happy, you might just adapt your old pages to mobile-friendly ones and serve them on a subdomain (e.g.,
Those pages can have the structural changes that you're thinking about, such as using responsive elements like div's with CSS, instead of rigid tables. Thus you'll be providing an updated design, while expanding accessibility - and you won't have to be concerned about changes in SERP or otherwise to your main website.
Alternatively, you can implement those changes in your current pages to make them more responsive and optimized, leaving the content intact so that your SERP is also not affected. For more about this from an SEO-perspective, take a look at: Responsive Design & Mobile SEO: Best Practices for 2013
There are many tutorials on the web showing how to approach responsive web design, here's just one: Responsive Web Design
Lastly, in consideration for updating your site's code, you might want to test if it meets current W3C standards or not, which can be done using their online validator: W3C Markup Validation Service You can also test how it appears in recent browsers using Browser Shots.
In short, I wouldn't feel compelled to redesign a site just for the opinion of future developers, unless there are significant issues that are impacting its use (i.e., it doesn't conform to W3C standards, or appears incorrectly in current browsers). A better reason to do this would be to think about potential visitors and their user experience, taking into consideration growing trends in technology like mobile access.