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.
In Old Norse, Ratatoskr means "drill-tooth" or "bore-tooth". It is the name of a mythical creature, a squirrel that runs up and down the tree of life called Yggdrasil, acting as a messenger between two arch enemies: the great eagle and the terrestrial dragon.
According to Albert Sturtevant, "[as] far as the element Rata- is concerned, Bugge's hypothesis has no valid foundation in view of the fact that the [Old Norse] word Rata (gen. form of Rati*) is used in Háv[amál] to signify the instrument which Odin employed for boring his way through the rocks in quest of the poet's mead [...]" and that "Rati* must then be considered a native [Old Norse] word meaning "The Borer, Gnawer"
Wikipedia
One can therefore assume that the word rat stems from a description of its behaviour.
Best Answer
OED confirms that it is from Tibetan sharpa, inhabitant of an eastern country. The other forms listed are Serpa, Sharpa and the earliest forms recorded are Serpa and Sérpá from 1847.
The following excerpt is from an article titled "Sherpa History" from the official site of Tapting (a village development committee in Nepal) and explains the origin of sherpa with historical references and citations from ethnologists.
However, I did some research regarding your theory about sher being lion in sherpa and I could find some hints related to Thakali language (Thakali is one of the ethnolinguistic groups in Nepal along with Sherpa and these two groups share the same region in Nepal). (see map).
The first reference I could find is about the Thakali clan Sercan which has a lion on their emblem; and the root of the word is mentioned as ser- which suggests that it might mean lion. (from the book Himalayan Anthropology: The Indo-Tibetan Interface edited by James F. Fisher):
Note: Snellgrove is a tibetologist and Oppitz is an ethnologist.
I continued my research by focusing on the term Sercan and I could find another form of the term which is Shercan. It is one of the four Thakali clans and the clan protector is mentioned as the white lion of the glaciers. (from the publication Ritual practice and group maintenance in the Thakali of central Nepal by Andrew E. Manzardo)
Then, I could finally find a source that actually says sher means lion in Thakali language. (from the book The Thakali: a Himalayan ethnography by Michael Vinding)
On the other hand, lion is senggi in Sherpa language (from Sherpa-English English-Sherpa Dictionary by Nicolas Tournadre, Lhakpa Norbu Sherpa, Gyurme Chodrak & Guillaume Oisel):
Oh! Let's not forget pa. This Tibetan affix strongly suggests that it is related to people in the word sherpa, although it is a very versatile affix that can be used in a variety of ways. The below excerpt is the definition of pa from A Tibetan-English Dictionary with special reference to the prevailing dialects By H. A. Jäschke:
In conclusion, the accepted etymology of sherpa is Tibetan sher (east) and pa (people or inhabitant) but there is a good evidence that sher might be related to lion based on the above findings.