We might have to do some "fiddling"
It is sense 4 of the verb fiddle per the OED. It has been around since at least 1630 and Daniel Defoe was using it in 1703.
Interestingly the nounal use is said by the OED to be of US origin, and dates from more recently.
Verb
- trans. and intr. To cheat, swindle; to ‘wangle’, intrigue; (see also quot. 1850). Also with into, out of. Now only slang.
1630 T. Dekker Second Pt. Honest Whore v. ii. 117 There was one more that fiddled my fine Pedlers.
1703 D. Defoe Villainy of Stockjobbers Misc. 268 There People can..Fiddle them out of their Money.
1738 Ld. Chesterfield in Common Sense 14 Oct. Somebody else would have been fiddled into it again.
1850 Lloyd's Weekly 3 Feb. (Farmer), I understand fiddling—that means, buying a thing for a mere trifle and selling it for double or for more.
1851 H. Mayhew London Labour I. 424/2 The way the globe man does is to go among the old women and fiddle (humbug) them.
1861 H. Mayhew London Labour (new ed.) III. 130/2 We are generally fiddled most tremendous.
a1889 St. Louis Chron. in Barrère & Leland Dict. Slang (1889) I. 360/1 Bob is the man who fiddled himself into Congress.
1938 F. D. Sharpe Sharpe of Flying Squad xv. 169 They fiddled into this job.
1955 Times 12 Aug. 5/4 William Alfred Powell, in evidence, said he approached Heard about getting a letter ‘fiddled out’ for him.
1958 S. Spender Fool & Princess 172 His own power for ‘fiddling’ through... His capacity for making deals.
Noun
f. A swindle. orig. U.S.
1874 Hotten's Slang Dict. (rev. ed.) 160 Fiddle... In America, a swindle or an imposture.
1947 People 22 June 4/2 Says Bevin: ‘I want peace..and we shan't get it unless we deal with one another as friends. I will be a party to no fiddles.’
1958 G. Mitchell Spotted Hemlock xi. 117 Tony and I can do something about it on our own. Not a fiddle, I don't mean.
1959 Spectator 4 Sept. 297/2, I know you'll think this is one of my fiddles. At my last parish we raffled a horse and trap,..a clothes horse and a mousetrap.
This is certainly a timely question for readers in the United States: The final day for citizens to file their federal and state income tax returns without incurring a penalty for late filing is April 15. In the spirit of the impending dismal day, I'll focus on Mari-Lou A's third question:
3. Do Americans fiddle their taxes? What's the American English slang for not paying taxes?
One somewhat old-fashioned slang term still in use in the United States for cheating (on taxes or in other areas of opportunity is chiseling. From Wil Haygood, "Rep. Charles Rangel reflects on his censure and his legacy" in the Washington Post (January 30, 2011):
How did one of the shrewdest operatives in the House of Representatives, a man who rose to become chairman of the most powerful committee, Ways and Means, an expert in tax law and spending procedures, a hero to black America, get caught chiseling on his taxes? How did he let himself become the latest example of ethical lapses in Congress?
According to the article, a House ethics committee found that for 17 years Rangel had not paid taxes on property h owned in the Domincan Republic, "and it concluded that he had accumulated more than $500,000 in undisclosed financial assets."
A second slang term sometimes used is cooking, as in "cooking the books" or "cooking the accounts." From "Cooking the Books," in The Progress Report (September 21, 2012):
Earlier this year, [Mitt] Romney said he had paid at least 13 percent in taxes every year for the past decade. The truth is that his tax rate for 2011 would’ve been around 9-10 percent. So today Romney cooked his tax return and used an accounting trick to pay more than he actually owed in order to generate better headlines.
A third slang term is stiffing. From a letter to the editor in C.F.O., volume 22 (2006):
Ingersoll Rand, a company headquartered in Bermuda to avoid expenses by stiffing the government for federal taxes (as do Accenture, Tyco, and so on), is distraught that there were not enough skilled workers available to get their contracted work done on time. This smacks of a convicted bank robber complaining about not being able to open a checking account.
A fourth option is the term doctoring, as in this headline from the Staten Island Advance (November 24, 2008):
Staten Island tax preparer fined for doctoring tax returns
And a fifth is bilking. From Stacey Edgar, Morality and Machines: Perspectives on Computer Ethics (2003):
The president of Quik Tax Dollars, Inc., a major nationwide tax-preparation service, was indicted on charges of bilking the IRS [Internal Revenue Service] out of more than $1.1 million in a tax fraud. He apparently created 145 false tax returns, complete with names and Social Security numbers (shades of "dead soul in the computer) and used an intermediary company to forward the bogus returns electronically to the IRS.
More euphemistically we have the wording "shortchanging the government." From Philip Ryken, Ecclesiastes: Why Everything Matters (2010):
Envy is not the only reason that people work, of course, and if we took this verse [Ecclesiastes 4:4: "The I saw that all toil and all skill in work come from a man's envy of his neighbor. This is also vanity and a striving after wind."] by itself it would sound like an exaggeration. There certainly are some exceptions that prove the rule. But the Preacher still has a point—one of the reasons we work so hard is to get what our neighbor has. This is why some people shortchange the government on their taxes, or cheat their customers, or get into debt with their credit cards. It is because we envy what other people have and will do anything to get it.
No wonder fiddling hasn't caught on in the United States—there's no room for it. I should note, however, that by far the most common phrase used in this country for the activity is the prosaic but accurate "cheating on [one's] taxes"