To answer your question, there is no “best way in wordpress”, as rounded corners have nothing to do with the CMS, itself.
As for IE, it has been a pain for web developers since day one. Unfortunately there’s still a sizable number of people out there using it, but that number is declining. I spent years playing “whack-a-mole” with the various browsers and finally realized how futile it was.
If you really need your website to look the same in every browser, then you might want to consider using the old CSS background image hack for displaying rounded corners (do a Google search and you’ll find endless tutorials on the subject).
However, the contemporary approach to web design is that it’s okay if a website doesn’t look exactly the same in every browser, as long as it doesn’t affect the overall user experience. Rounded corners isn’t a necessity, so I personally wouldn’t spend that much time on it.
It all comes down to ROI. Is it worth the extra time (i.e. money) to fuss around with the idiosyncrasies of the various browsers? In billable hours, how much time have you already spent on this? If your customer is so worried that not having the corners rounded in IE will make or break the deal, then he or she has probably lost focus on what’s important: the message, or content.
Believe me, visitors don’t care about minor differences in decorative features. They will quickly leave the most beautiful website in a heartbeat and never return if they don’t find what they’re looking (often within seconds).
It’s up to you, but as the owner of a web design company, I explicitly tell my customers up front to expect minor differences in appearance between browsers. While I’m more than willing to spend the extra time (if they’re willing to pay for it), astute customers realize it’s totally unnecessary because they expect to have more to offer visitors than pretty bevels and dazzling gradients.
I’m not saying this to be condescending. Hopefully it’ll help you focus on what’s important. I wish someone had said this to me a decade ago because I wasted a lot of time fumbling around with unnecessary tasks until I started thinking in terms of the business aspects and reading the advice of veterans in the industry.