Learn English – the meaning of “shall we say” here

Have you ever noticed when someone is speaking, and the speaker comes to a particular word or phrase, and then pauses to wink at the person they are talking with? Sometimes that wink might mean, "I'm just joking here," but sometimes it means a little bit more than that. Sometimes, the wink suggests:

There's more I could say here – you know that, and I know that – but you and I have a mutual understanding, so there's no need to elaborate any further.

That is the essence of the inserted shall we say.

I'm reminded of a skit my daughter and her friends wrote and performed for their school history class. Their topic was the role of women in the U.S. Civil War, and they wanted to portray what one blogger describes as:

Women .. were excellent Civil War spies. Women were not seen as threats, and they could turn to seduction to get what they wanted. According to Winkler, they "tucked coded letters into their skirts, dressed as men, pretended to be grieving widows and seduced enemy officials to get and pass information."

In the skit, my daughter pulled a note from her bosom, shared the information, and then, before departing, said to her co-conspirator:

I'll be back; right now, I need to go get some more [*wink*] information.

Sometimes we might use the term quote-unquote to convey the same sentiment, or use "finger quotes" to do that with a visual cue:

"I'll be back; right now, I need to go get some more, quote-unquote, information."
"I'll be back; right now, I need to go get some more..." [pause and use finger-quotes] "information".

Another way she might have said that is:

I'll be back; right now, I need to go get some more, shall we say – "information".

No matter how it's spoken, or what visual cues are used, the sentiment is the same:

You know exactly what I mean when I say "go get some more information" – I don't need to go into the lurid and scandalous details.

Back to Angels and Demons (which is a sequel to The Da Vinci Code), where the speaker says:

Your expertise. Your erudition. Your recent involvement with certain church, shall we say, mysteries!

Here, the person being spoken to (Langdon) has indeed learned a lot about church's... What shall we call them? Mysteries? One word seems hardly adequate; it's a very tangled web. At any rate, the speaker and listener both know about all the secrets and conspiracies that were uncovered during Landon's previous adventures. By inserting the phrase shall we say before the word mysteries, it's as if the police inspector is saying:

This is long and complicated, but I'm going to just sum it up in one word – mysteries – which is probably inadequate, but you and I both know full well what I am talking about.