Catch Evolution is indeed a wordpress theme so I'm not sure what you mean by "not of WordPress." So no issues there.
Do you mean does the redesign impact search traffic or other kinds of traffic? Well, there's two parts. There's the user experience, meaning some may get lost if it's not user friendly and then there's Google traffic. There shouldn't be much of a change in the latter unless your main content is drastically different and/or Google has trouble spidering/reading your main content.
Remember, SEO is not just about on-page stuff anymore, it's authority and the bigger picture. Onpage definitely still matters but not as much.