I'm going to invite my fiance's friend to the wedding without inviting friend's wife.
Why do you only want to invite the friend and not his wife?
My friend's wife is an awful person who secretly hates me.
It's very rude to exclude your friend's spouse from an event like this. When you invite someone to an important function, it is commonly understood that you are inviting the spouse along as well. It would be best just to tolerate her presence to avoid upsetting everyone.
That's ridiculous! I'm going to invite her husband even if I can't stand her and now I'm ranting on this chat.
It's better to deal with it, or perhaps not invite the friend either.