All Praise is for Allah.A man holding his wife’s hand while walking: Basically, there is nothing wrong with it and none of the spouses is sinful for doing this. On the contrary, it may serve a purpose, e.g. if they are walking in crowded streets etc.
However, in these matters one should also keep in mind the values of the people of that area. If it is something which is commonly done by chivalrous and honorable people, then there is nothing wrong with it. But if doing so causes people to find fault with the chivalry, manners, morals or character of the person who does this, such that only sinful people, disbelievers etc. of that society are known to do such things, then the couple should not do so in public.
Also, holding the wife’s hand in the street may be acceptable according to the social norms, as when most people commonly hold hands it is generally taken to mean she is being escorted or helped etc. This is different from the way immoral people hold the hands of their girlfriends, which is a type of fornication of the hand. Hence, one should beware of taking in things which are basically permissible, or taking it to a level which resembles flirtatious behavior.
Allah knows best.