Any of those options will work, but if you refer to words more than once you should take care to use the same convention in each place. Italics seem the best option if you can use styled text, but styles aren't always available.
In American English, it's conventional to place punctuation marks inside quotes instead of outside. There are a lot of situations where that practice leads to ambiguity, though, such as when instructing the reader to type something:
Click in the text field and type "salami".
It's good to know the accepted convention and follow it when possible, but convention should take a back seat to clarity. A typographic convention, such as using italics instead of quotes, can solve the problem by eliminating the quotes, but even then it's not always easy to tell if a punctuation mark like a period is italicized or not:
Click in the text field and type salami.
The swung dash is most often used to omit something obvious from context for the sake of space. A common use as such is in dictionaries where it can stand for the word currently being defined, though it can also be used as a more general "ditto" mark, to mark information that is omitted or unavailable in transcribing a damaged text, and so on.
As pointed out in another answer, Japanese uses wave dashes (〜) in ways that are analogous to some uses of other dashes in English, such as how the en-dash (–) is used for ranges (1m-2m in English, 1m〜2m in Japanese) and this particular case can sometimes be seen on specification labels on equipment as it stands out a bit more.
That said, it isn't used so much for parenthetical uses of the dash, and the wave dash (〜) is not the same as the swung dash (⁓), so this seems doubtful, though not impossible; borrowings from other cultures and languages aren't always faithful to the source, and certainly uses of punctuation in one language has influenced its use in English whether as a widespread use (e.g. the apostrophe comes from French use, and is now fully a part of English punctuation including in many cases where it does not match French use) or more restricted to a particular community (e.g. the fondness many early-mid 20th Century modernist writers in English, particularly Joyce who insisted adamantly upon them, of the use of em-dashes as speech markers owed a lot to French use—no doubt at least partly related to the number of said writers who lived in Paris).
In all, I can't say this is a standard use, and I can't recommend it: As someone who is used to the swung dash the examples in the question read to me as confusing nonsense because I can't figure out what the words omitted are. That is, I read:
*You are the friend ~ the only friend ~ who offered to help me.
As
You are the friend [text left out] the only friend [text left out] who offered to help me.
And I can't see what that left out text is likely to be here.
Edit:
stib points out that a reasonable reading if one was familiar enough with this cartoon to have remembered it, is:
You are the friendbeast the only friendbeast who offered help to me.
It even explains the lack of commas. The further that is from what was intended (including the missing commas), the more inadvisable it is.
Best Answer
Who ''coined'' the term “scare quotes”?
This appears to have originated amongst British logical philosophers in the late 1950s and early 1960s.
According to the Oxford English Dictionary, the earliest known use is from Mind 65 in 1956. Here it is with more context:
This is a paper by G.E.M. Anscombe (1919 – 2001) called “Aristotle and the Sea Battle”. Elizabeth Anscombe was a professor of philosophy at the University of Cambridge and collaborated with and was married to Peter Geach (born 1916).
Geach also used the term in Mental Acts: Their Content and Their Objects (1957) (reprinted 1971):
Other early uses:
The Aristotelian Society's 1963 Supplementary Volume. I believe it was used in a paper called Symposium: Plato and the Third Man by Colin Strang and D. A. Rees, who acknowledge Geach (amongst others) and apparently Anscombe's name is on the following page.
Montgomery Furth in his 1964 introduction of his translation of Gottlob Frege's The Basic Laws of Arithmetic, and mentions Geach's translation of Frege on the same page.
From 1965 - 1970 some 20-odd other books, spreading from logical philosophy to ethics, theology, political and legal philosophy, political science, language and metaphysics, and to America and Australia.
Use continued in the 1980s but was on the whole restricted to these and related fields, and in the 1990s seems to have spread further within academia, but not much outside; the earliest news source I found using it was a 1994 Newsweek with other s using it once each in 1996, 1997 and 1998.
Why is the word scare used?
Because the writer is afraid to use the term directly, and places it instead in quote marks to attribute it to another.
For example, "This is a news website article about a scientific paper" from the Guardian:
1946
Edit: Dan Bloom has sourced a 1946:
The book by Carey McWilliams is Southern California: An Island on the Land and on page 298:
This edition is copyright 1946 and 1973 by McWilliams, but a search on Hathitrust appears to verify it in a 1946 edition.