c. Phr. to cramp one's style: to restrict one's natural actions or behaviour.
[1819 LAMB Let. 7 June (1935) II. 250, I will never write another letter with alternate inks. You cannot imagine how it cramps the flow of the style.] 1917 A. WOOLLCOTT Let. 2 Sept. (1944) 26, I think the very fact of a censorship cramps one's style. 1919 Punch 9 Apr. 283 (caption) Cramping his style. 1923 Saucy Stories 1 Nov. 124/1, I always go out with Edith... Edith never cramps my style.
but Google Books finds many more examples, showing it to be well established in the fully modern sense pre-1920, and even earlier (e.g. 1800-1900) applied to handwriting, physical or literary style ("cramp", then as now, means "constrain" in this sense) such as
"freed from that dry severity of ratiocination which never fails to cramp the style of ordinary mathematicians, when writing on theological subjects."
- Horsley's sermons, The Quarterly Review, William Gifford, John Taylor Coleridge, John Gibson Lockhart, William Macpherson, William Smith, John Murray. Published by J. Murray, 1813
and even down to the early 1700s, in an anonymous poem congratulating John Dryden on his translation of Virgil and taking a dig at earlier Dutch translators, particularly Joost van den Vondel:
The heavy Dutchmen, with laborious toil, Wrested his sense, and cramp'd his vig'rous style.
- To Mr Dryden on his Excellent translation of Virgil, The Works of Virgil: Containing His Pastorals, Georgics, and Aeneis By Virgil, John Dryden, Knightly Chetwood. Translated by John Dryden. Published by Printed for J. Tonson, 1721
It's probably even pre-1700, since Dryden's The Works of Virgil came out in 1697, and the anon poet wouldn't have waited 20+ years to write a fan letter. Of course, this doesn't quite resolve the problem. If a usage grates with the audience because it's widely perceived as an anachronism (even though it isn't) should a writer risk using it? Difficult: I'm with historical precedent all the way, but it's a somewhat political decision if the writer isn't solely in charge of the choice. See the Comments for further discussion.
In a similar vein to the above excursion, I've enjoyed linguistics blog Language Log's etymological detective threads such as Did Plato say this? (tracking an apparent fake attribution of an epigram to Plato), Every little (bit?) helps (another back-tracking of an apparently modern expression), the previously mentioned Giveth and taketh, and Mumfordishness: an appeal (who was Mumford?).
Where did people go to get historical-etymological questions answered before Google Books and web forums like Yahoo Answers? Notes and Queries. This is not its modern relative in the Guardian (interesting though that is) but the far more venerable journal described in A Victorian virtual community (Patrick Leary, Victorian Review, Vol. 25: 2 (Winter 2000) 62-79. In comparison with Tom Standage's The Victorian Internet (which argues a convincing analogy, technologically and culturally, between the Internet and telegraph), Leary likens the 1849-founded Notes and Queries to the Internet forum ("N&Q provided access to an unparalleled flow of textual information within a community defined by the terms of that exchange" - and to be blunt, those terms were sheer geekiness of interest ("minutiae about old manuscripts, obscure incidents, forgotten customs, and local lore"). It's rather at the level of Cecil Torr's Small talk at Wreyland, and it's unsurprising that Torr's books were advertised in the journal and frequently cited.
It's wonderful stuff. The 1849-1869 editions are digitised here at the Internet Library of Early Journals; and some, in more convenient plaintext format, are at Project Gutenberg. The journal Notes and Queries, its flavour not much altered, does still exist as a subscription journal from Oxford University Press (home page here, from which you can access a full archive of contents lists).