Why is it “knife” in the idiom, “Before you can say knife” though there are many shorter words than knife?

I saw the phrase, ‘before you can say Dow-Jones Index’ in the following sentence of JefferyArcher’s novel, “Not a penny more, Not a penny less.”

Scotland Yard’s Fraud Squad Detective Inspector, Clifford Smith tells young Oxford's visiting Mathematics professor, Stephen Bradley who fell a victim to a large scale investment fraud, being coaxed by his Harvard school mate:

“I’m sorry to say that we can hardly ever recover the money, even if we produce enough evidence to nail the villains. They have it all stashed away all over the world before you can say Dow-Jones Index.

I guess “Dow-Jones Index” here is Archer’s version of “before you can say knife (or Jack Robinson),” but I’m curious to know;

1) Can we coin and use as many variation of “before you can say X” in our conversation as Archer did?

2) Is there a standard or best received pattern of “before you can say X”? Is it “before you can say knife”?

3) What is the origin of “before you can say knife”? Why it should be the “knife,” not gun, sword, Tom, Jon, any other words that represent for brevity?

Solution 1:

1) Theoretical answer is yes. You can coin as many words as you want to create your own version of "Before you can say Jack Robinson" You might use that to talk about a character or object that appears in the book to give it a personal touch. Though if you use an other words than "knife" or "Jack Robinson" the meaning of the original Idiom may be misunderstood.

Usage notes: Often the word or phrase that follows before you can say is related to the situation you are talking about: In summer, food goes bad before you can say heat wave

2) The standard idioms are:

before you can say knife
before you can say Jack Robinson
before you know it

3) Where the Idiom with "Jack Robinson" came from:

This expression originated in the 1700s, but the identity of Jack Robinson has been lost. Grose's Classical Dictionary (1785) said he was a man who paid such brief visits to acquaintances that there was scarcely time to announce his arrival before he had departed, but it gives no further documentation. A newer version is before you know it, meaning so soon that you don't have time to become aware of it (as in He'll be gone before you know it). source: wiki

before you can say “knife” This colloquial British expression is equivalent to before you can say “Jack Robinson.” Mrs. Louisa Parr used it in Adam and Eve (1880). source

::Edit big thanks to abhinav for the origins of before you can say knife

Solution 2:

To elaborate on question 1), it's reasonably common to replace Jack Robinson with a "humorously appropriate" phrase for the situation at hand, such as your author did when talking about money from investment fraud being stashed.
Some other completely made-up examples:

When she found out her new boyfriend had a criminal record, she dumped him faster than you can say habeas corpus.

The 5-year-old grabbed the stray lollipop and bolted off to his room faster than you can say 'Willy Wonka'.