I agree that both sound idiomatic, but there's a subtlety : "take + [action]" and "take + [object]".
Here, a "hymeneal tour" is an action, something you do, not an object you take. And taking about an action, it makes more sense to say "He wants do it" rather than "He wants to have done it", right? What you want is to do this thing, not to have done it.
Here's an example:
He would have liked to take a ride in the rollercoaster.
He would have liked to have taken his phone with him, the meeting was way longer than he expected.
In the first one, what you want is the action, being in the rollercoaster. In the second one, what you want is having your phone, the result of the action, not the action of taking your phone. The emphasis is on the action being done and not on doing the action.
In the text, what he would have liked is the action, not the result.
That's how I see it. I don't know if there's a grammatical truth behind it, but to me it makes sense to see it that way.