Very true, crocodiles do spend a lot of time in the water, however, I'll bet most don't use moisterizing soaps, anti-fade hydrate shampoos & conditioners, daily thermal mini-peels and such. If they did, they wouldn't have very crocodile-like leather for very long, would they? I agree with your wife, keep the leather watch straps out of the shower.
I never quite understood why anyone would want to wear their watch in the shower anyway. OK, I can understand if you wear a watch to the gym and then shower, not wanting to take the watch off for fear of losing it or worse, but other than that, I guess I don't get it. I see people on TV also wearing their watches to bed. Huh? OK, maybe if it's a spur of the moment thing, but generally, no. Just my opinion.