A friend of mine who used to be in the (British) Army once mentioned in passing that a particular NCO would “take you for a little run” rather than deal with discipline issues officially. I took this to be a euphemism, and I’m glad I never found out exactly what it was for.
One from the nicer end of the spectrum: on the Great British Bake-Off, judge Mary Berry used to use the phrase “rather informal” when what she meant was “what the fuck is that?” 
My favourite source of alternate phrases is probably Yes, Prime Minister. But not all of these are euphemisms, even if they are both courageous and novel.
My favorite these days is from Brockmire:
Big brown bear knocking at the back door
In the Red Sparrow spy trilogy, some British spies in Hong Kong spoke of an incompetent boss as FIGJAM.That stood for “Fuck, I’m Great, Just Ask Me.”
That was Phil Mickelson’s nickname amongst his fellow professional golfers.
Years ago I was in mixed company when one of the women excused herself, saying she had to “go and use the facilities.” After she had left I wondered aloud why she couldn’t just come right out and say she needed to take a leak.
One of the other women responded, “maybe she needed to take a shit.”
Are you sure you didn’t mean Yes, Minister? I thought this earlier series was more fun than its successor, all the more so because Hacker was beset both from the bottom, by the civil service, and from the top, by the Prime Minister’s Office. And I’m pretty sure that Yes, Minister was where the euphemism of a “courageous decision” came from.
You’re right. In my own mind, FWIW, when I said that I meant both series - which I view as a continuum. Both books and series were great fun.
I usually say, ‘Excuse me. I have to urinate.’ I think Mrs. L.A. doesn’t like it.
“Tree frogs”
The pink slip in English turns into a blue letter in German, at least in Switzerland.
I prefer “tap a kidney”.
I had a design professor who, if she didn’t like a project, would say “Well, that’s a choice.”
And I grew up with the same meaning applied to a similar expression, “I’m going to see a man about a horse.”
I just recently saw the term “nervous shock” used by Trevor Noah’s lawyers in a suit he is filing against an orthopedic surgeon. I learned about all kinds of shock in medical school. Septic, hypovolemic, cardiogenic, anaphylactic, and even neuorgenic. Nervous, however, wasn’t one of them.
Those little dried chili peppers you find in Asian dishes? In Korean they’re called gochu, which is also the Korean euphemism for a little boy’s penis. I’ve always felt English sadly lacked that distinction out of the belief that a pre-puberty penis becomes a different item after it begins to have erections and pass fool-juice as well as urine. At any rate, pre or post puberty, Chachi is not a word for penis, unless we referring specifically to Scott Baio.
Ahhhh…but the correct lyric for (that farty girl) Windy is:
“Who’s tripping down the streets of the city”
I know this because as 8 year olds, my best buddy and I were titillated to hear: “Who’s STRIPPING down the streets of the city”.
The idea of a woman casually breaking public nudity taboos being celebrated in a pop song seemed pretty awesome to us
There are more layers to this one than you realize, because “toilet” is, itself, a euphemism for that fixture. In fact, nearly all of the terms for both that fixture and the room in which it is found are euphemisms.
Hah, that’s funny, I didn’t know that idiom. There’s an equivalent expression in German: “mit Kurt und Jörg telefonieren”, “having a call with Kurt and Jörg”.
Calling Earl.
My mother actually tends to call that fixture “the euphemism”.