One of my cousins is hosting a "Couples' Shower" for my fiance and me, and both sets of friends (single and married) are invited. She says it's the "new" thing to do.

Whatever! But if I had to choose, I would prefer a shower. I'm not big on parties to begin with so I wouldn't feel as though I was missing anything.
My fiance has made it clear he does not want a bachelor party, but his groomsen have other plans. I would not be upset if he attended a bachelor party because I'm secure in my relationship and trust him completely.