A kittly-bender is « an area of yielding or broken ice on a body of water; also fig; hence v phrr run kittly-benders, play at ~ to run or skate over such ice as a sport » (DARE):
1871 Hale How to Do It 46 ceMA, You will, with unfaltering step, move quickly over the kettle-de-benders of this broken essay.
What does the author mean here? What are the kittly-benders of an object (that is not ice)?
As you have discovered, kittly-benders means “thin ice.” Under kittly, adj. in the Oxford English Dictionary, we find (along with your example sentence):
b. kittly-benders n. kettle-de-benders n. thin ice which bends under one’s weight; the sport of running over this. (U.S. colloquial.)
1854 H. D. THOREAU Walden 353 Let us not play at kittlybenders.
1872 E. E. HALE How to Do It iii. 46 You will, with unfaltering step, move quickly over the kettle-de-benders of this broken essay.
Source: Oxford Enlish Dictionary (login required)
The author of your example uses kittly-benders figuratively here to suggest that reader will be able to get through his essay despite the “danger” of its verbosity and rambling asides (the thin ice of writing style). Here is an expanded excerpt from Hale’s work:
Have you all read, and inwardly considered, the three rules, “Tell the truth”; “Talk not of yourself”; and “Confess ignorance”? Have you all practised them, in moonlight sleigh-ride by the Red River of the North,—in moonlight stroll on the beach by St. Augustine,—in evening party at Pottsville,—and at the parish sociable in Northfield? Then you are sure of the benefits which will crown your lives if you obey these three precepts; and you will, with unfaltering step, move quickly over the kettle-de-benders of this broken essay . . .
Here it is paraphrased:
Have you inwardly considered the three rules . . . ? Have you all practised them . . . ? Then you are sure of the benefits if you obey them; and you will, with unfaltering step, move [skate] quickly over the kettle-de-benders [thin ice] of this broken [fragmentary; imperfect] essay . . .
The OED has an entry for kittly, adj.
Etymology: < kittle v.1 + -y suffix1; compare Norwegian kitlug , Swedish kitlig , Low German kitlich , German kitzlich . For the sense ‘risky’ in the compound kittly-benders , compare kittle adj. below
a. Easily tickled; susceptible or sensitive to tickling; ticklish; tickly.
1830 J. Galt Lawrie Todd (1849) v. ii. 199 It made the very soles of my feet kittly to hear it.
(The entry for kittly-benders n. kettle-de-benders follows and is in agreement with your example:
b. kittly-benders n. kettle-de-benders n. thin ice which bends under one's weight; the sport of running over this. (U.S. colloquial.)
1854 H. D. Thoreau Walden 353 *Let us not play at kittlybenders. * 1872 E. E. Hale How to Do It iii. 46 You will, with unfaltering step, move quickly over the kettle-de-benders of this broken essay.)
This takes us to kittle, adj.
Ticklish; difficult to deal with, requiring great caution or skill; unsafe to meddle with; as to which one may easily go wrong or come to grief; risky, precarious, ‘nice’, delicate.
1568 in J. Cranstoun Satirical Poems Reformation (1891) I. xlvi. 60 Scho will be kittill of hir dok.
1869 C. Gibbon Robin Gray xiv Metaphors are kittle things to handle.
1890 Truth 11 Sept. 526/2 Cleopatra is a kittle character for a London theatre, unless played by some French actress who has no character to lose.
Bender is more obvious = that which bends.
kittly-benders n. = kettle-de-benders a part of the ice that bends and thus presents a risk.
It's worth noting that "ticklish" (adj.) has the same dual meaning of "kittly":
a. Easily tickled; sensitive to tickling.
1615 H. Crooke Μικροκοσμογραϕια 72 Some part of the skin is..thin, as in the sides and soales of the feete, which is the reason that there men are ticklish.
5. Liable to end in disaster unless treated with great care; needing cautious handling or action; delicate, critical, precarious, risky, hazardous.
1899 F. T. Bullen Log of Sea-waif 27 This is a ticklish evolution to perform successfully in a crowded anchorage.
