From the comments to the OP:
My understanding of the terms "hardcore" and "softcore" come from baseball and softball, and the term "hardcore" at least is roughly synonymous with "playing hardball" which is definitely baseball-related.
More in-depth: Since the early 1900s at least, baseball has been played with the eponymous cork-cored, twine-wrapped, leather-skinned sphere that has near-universal recognition. The only significant change to the "official" baseball used in the major leagues was during WWII when rubber was substituted as the core material to replace cork (which was needed for the war effort). Cork baseballs are small, dense, and not very forgiving; in fact, players have died from head trauma after being "beaned" and been forced to retire after making barehanded catches that shattered every bone in their hand. Such a ball is a "hardball", and playing with it is "hardcore baseball".
The game of softball is not that much newer (1887 vs 1845 for baseball), but it evolved from the game we have come to know as baseball to create a more "casual" game. The name "softball" came from the original construction of softballs; primarily similar to baseballs, but much larger (up to 16" in circumference) and more loosely wound. As the early balls broke in, they really did become soft, and the game was actually originally intended to be played barehanded (thus requiring virtually no individual equipment; just one bat, one ball, and some base markers). Modern softballs are not very soft, and so the modern game is played with gloves (and "fast-pitch" leagues for women use practically all the same gear as men's baseball leagues with the primary exception of "pelvic protectors" replacing athletic cups), but the balls still "give" more than cork baseballs, and more often incorporate softer core materials such as rubber.
The two games have both been around long enough in recognizable forms, along with the eponymous balls used to play them, to be the origins of the terms. My thoughts are that "hardcore" came first, and then "softcore" followed as a complementary antonym. Unfortunately the sexual connotation the terms have gained makes it difficult to do real research into the terms themselves from a work computer. I know the term "hardcore" has been commonly used figuratively since at least the Vietnam War.
Chiffy
"Etymologicon Magnum, or Universal Etymological Dictionary" by Walter Whiter (1800) makes the claim that "chiffy", as used in the term "in a chiffy" derives from the Anglo-Saxon word "Caf".
"A Dictionary of the Anglo-Saxon Language" by Joseph Bosworth (1832)
confirms the meaning of "Caf" as "quick, sharp, nimble, swift".
Jiffin
This is my oldest source yet, this time for "jiffin".
"The Fall of British Tyranny: or American Liberty Triumphant" by John Leacock
This was published in MDCCLXXVI, which by my reckoning is 1776.
Please to walk aft, brother soldiers, that's the fittest berth for you, the Kidnapper's in the state room, he'll hoist his sheet-anchor presently, he'll be up in a jiffin --- as soon as he has made fast his end of his small rope athwart Jenny Bluegarter and Kate Common's stern ports."
Jiff/Jiffy
In 1791, Edward Nairne of Sandwich, Kent published "Poems, Miscellaneous and Humorous, with Explanatory Notes and Observations" in which the following lines appear:
At dinner-time, and bus'ness slack,
I stept to Joe's, and got a snack
A pot of mildchee, and a whiff,
And off again in half a jiff !§
The author's explanatory notes, below, are expansive and delightful:
§ Jiff or jiffy, a jocular expression, and means a short space of
time. Innumerable are the expressions (particularly amongst sailors)
to shew what expedition may be, or is intended to be made, in the
doing of any act ; the progress of these is curious. I perfectly recol-
lect, when a school-boy, an expression of this kind — ' Before you
can say Jack Robinson' — was very common. After the intervention
of various others, that of — ' As soon as you can say peas' — came
into vogue ; but some persons, who were not over precipitate, very
properly qualified it by adding — ' and boil them.' Next, the ele-
gant expression of doing any thing ' In a pig's whisper' came into
fashion! (What particular period of time this contains, I am at a loss
to determine, having never yet had the pleasure of hearing these melodious animals exhibit in this way ! — I have frequently, and with
admiration, observed them make transitions from one note to another,
and which usually has a most charming effect.) — The ingenuity of
modern times has, I believe, brought this business to its ne plus ultra,
its greatest perfection ! and people can now, according to their own
declarations, do things ' In less than no time ' This beats Joshua's
making the sun stand still -, for that only protracted daylight, and
puzzled the clocksmiths ! but this has all the advantages of time,
without the inconvenience of waiting for it.
Best Answer
I propose that "no big whoop" (and the sarcastic "big whoop") is a mash-up derived from "not to care/give a whoop" (which dates back to at least 1904) and "no big deal" (which the OP researched and mentioned in the question).
The phrase a whoop and a holler meant a short distance (i.e. something of little consequence.) So, no big whoop means literally "That is of little consequence."
See the OED entry 1c for whoop below:
"Give a whoop" and "care a whoop" used to be much more popular and now in the last few decades "big whoop" has passed it according to Google Ngram.
EDIT: Is it right to interpret the origin of "big whoop" as a sarcastic variation of "whoopee" (see Josh's answer)? Seems to me that the following ngram is evidence that it is from "not to care/give a whoop" rather than "whoopee". I'd be interested in the rest of the community opining.