By all means, go for the 10-22. It is an excellent general purpose rifle that can be used out of the box for training, small game hunting and [if you subscribe to the "beats a sharp stick" school] self defense. It is a multi-generational gun with minimal care, and can be depended on in tough circumstances.
Additionally, it looks like a .22 rifle should look, a classic. This might help to win your wife over, or at least more so than something with an 'AR' designation that comes in a box marked 'SURVIVAL RIFLE'. By the way, it might not be such a good idea to try to hide it from here. When she finds it, it will put a big ding in the relationship/trust factor. Better you should bring it home and brag to her about what a great DEAL you got, and she knows that you wanted one, and that it will be put away safely until you TWO go shooting. Then duck. Think about the arguments she will bring up, and what the logical counter arguments are - and don't weave some fantastic TEOTWAWKI scenario - fighting off mutant zombies generally doesn't cut it, neither does the threat of government takeover, etc. Remember that when - or if - the S hits the Fan, that trust between you will be worth far more than any firearm.
The AR-7, on the other hand, is a special-purpose gun intended to provide small game or protection for the short time you are waiting for rescue. It is accurate enough and rugged enough for its intended purposes, but that's about it. Unless you do a lot of flying in the bush or engage in some other activity that would place a priority on light weight and compactness, you will be better served by a 10-22 in any of its variations.
BTW, I've been married over 40 years and have only bought one gun on my own. When I got home, the first thing I did was show it to the Mrs., along with a detailed explanation as to the circumstances of the purchase. She threw a bitch-fit to put it mildly, then agreed with me. And then wanted to go shoot it. Usually, we went gun shopping together.