Is a white one really going to make a difference? With every console I've ever owned, I stopped caring about how it looked after about a week. It's a machine that plays video games, I couldn't care less what colour it was and you shouldn't either. Will it being white make you play games betterr? No. If you want to return it and get the money back sure, but your wife might feel hurt. She probably thought you'd really like it and was willing to spend that much to make you happy. I get crappy gifts for Christmas and Birthdays all the time - stuff I don't want, but stuff that's also super expensive. My mother got a ludicrously overpriced leather briefcase for me once - I had no need for it, it cost almost 600 dollars and it was too heavy and bulky for me to take to the hospital every day. I still kept it, because she thought I'd like it and I didn't want her to feel bad (although I later tactfully and gently suggested that in the future she should actually consult with me as to what I needed rather than just assume I had a need for big, overpriced leather briefcases).
Keep your PS4. There are other games you might play on it. A white one is not gonna play your games any better and I guarantee you that in a week or two you won't even notice the colour, because the colour simply doesn't matter. It's not like you're gonna take your PS4 out in public and hold it aloft for all to see. My PS4 could be bright freaking hot pink for all I care, but I'd gladly take it if it was free.