大奥婚 is made of two words:
- 大奥 most likely refers to the movie 『大奥〜永遠〜[右衛門佐・綱吉篇]』. As you can see from the Wikipedia link, both 堺雅人 and 菅野美穂 starred in this movie.
- 婚 is short for 結婚 ("wedding").
So you could translate it as "An Ōoku Wedding".
In this question, you included a second (unrelated) question about 電撃. The relevant sense in 大辞泉 is the following:
電光のように、前ぶれなしに衝撃を与えること。「―的な結婚」
I don't see any particular reason to translate this use of 電撃 to electric shock in English. It's the first gloss listed in some dictionaries, but that doesn't make it the right translation. The reason many J-E dictionaries list multiple glosses is that, for many words, there isn't a one-to-one correspondence between the two languages. The best translation for a given term often depends on context.
How does that apply here? Well, this is a common metaphoric use of the Japanese word 電撃, but the English term electric shock is usually used literally, so we're better off finding another translation. Let's check some dictionaries:
The Green Goddess gives 電撃結婚 as a lightning marriage, so if you want to use a similar metaphor in English, you could phrase it that way. You can also translate it without relying on metaphor: the same dictionary gives 電撃的 as sudden and unexpected, and both the Kenkyusha College J-E and Progressive J-E give 電撃結婚 as a sudden marriage.