What excuses, sorry, explanations, should I have in my EDC for when my Wife discovers them?
You carry emergency gear primarily to help others in need. What if one of your wife's friends was thinking of doing something, perhaps something your wife would advise against, where certain supplies could drastically reduce the potential negative consequences? What if it were one of your adult children?
Need an excuse? I should say not. Rather you should, with maximum subtlety and indirection, allow your wife to wonder why she does not carry such things as a concerned and prepared friend and parent.