Look for a gently used Ruger standard auto, preferably in stainless. Even a new one will probably cost a lot less than that PPK/S, which will be unreliable in most examples. Some do work okay most of the time, but only with high speed loads. I've read posts by men who say that only the hyper velocity ammo like Stingers will cycle their Walthers.
German police experienced an average of one jam per 50 shots fired from 7.65mm PP and PPK arms. The .22 version is even less reliable, on the whole. You might get a good one, but it's a dart toss.
The Beretta M87 and their earlier .22's about the size of their.380's have a good rep. See the post here by SIG P-220 about his Beretta M-948. If you want a small gun in this role, I think these little Berettas are your answer.
But your basic .22 should be a Ruger, unless there's some reason not to, and I can't think of any. You'll also find them a lot cheaper than the PPK/S, and generally a lot more reliable.
Try to find a MK II or the earlier one. I don't like the long loaded chamber indicator in the current MK III. It probably works okay, but damages the looks of the gun and is another place for powder fouling to accumulate.
S&W has made .22 autos. I wouldn't own one. Men who have them seem to experience a lot of jams. The looks aren't too special, either.
If it makes you feel better about the 007 angle, Ian Fleming owned a Ruger MK I .22 and I think had it in mind when he equipped a character with a long barreled .22 pistol.'