I actually laughed when I read seed guard... I don't mean that in a bad way, just that only manufacturers of bird cages want you to believe seed guards REALLY work... They may catch a few things, but honestly, unless the seed guard is a 3' radius around the cage, won't make that much difference.
Your best bet is to put down a mat or such under the cage that is easy cleaning and just be prepared to vacuum multiple times a day. I laugh that so many photos Victoria (Riddick07) posts of her birds, you can see the vacuum... and never in the same spot... It seldom gets put back into the closet, I use it that often.... and even then only when Ivory is in her cage and covered does the floor not get messed up. Someone posted on the forums a question, what do you sacrifice for your birds, my first thought - a clean floor!
One green cheek won't make a huge mess, but it will be enough (seed guard or not) that you will need to vacuum at least once a day, especially if you are in an area where ants can be a problem. I put down newspaper on the floor under Ivory's seed bowl and favorite hangout spot for easier cleanup, but that is more for poop then food. And yes, all birds fling food... Conures may be small, but they pick up food with their feet and eat, and when they are bored with whatever that item is, it gets tossed or dropped... and nutriberries bounce and roll pretty dang far!
I would not recommend sharing this with your wife if mess is her worry... let her fall in love with the little guy first, then hopefully she will be more inclined to just clean up behind him then be a problem about having a bird... its been my logic with having a kid... gave up years and year ago trying to convince Victoria she can put her dirty dishes into the dishwasher...

I am so gonna pay for that... but she knows its true.