What a wormhole!
I did a bit of digging on the term "Hindu" with some interesting result (posted below).
But before going any further, I wondering if Max had an opinion about using the term "Hindu Shuffle." You have already expressed you didn't think it a slur, but what of historical accuracy and credit?
Anyway, for the curious...
As to the word itself. Indeed there is a connection to the "sindhu" as Max stated. And there is connection between the word "Indian and Hindu" like I stated, but a bit reversed so it is indeed not a truncation. Still, it was a name applied to them by outsiders, but long before the British.
The Oxford English Dictionary traces Hindooism to an 1829 reference in the Bengalee, 45. It also refers to an 1853 usage by the German Indologist Max Mller. The adding of an "ism" made it a "catch all term."
In ancient India you had either a yogi, a bhakta, a tantric, a sanyasi, a sankhya vadin, a vedantin, a lokayata, a rishi, a muni, a pandit, a pragna, a yogini, a devi, a swami, a Saivite, a Vaishnavite, a siddha or Buddha,
but no Hindu.
No Hindu ever coined them.
The Hindus were even unaware of such a terminology for a very long time.
The earliest reference to the word "Hindu" can be found in the Avestha, the sacred book of the Zoroastrians. The word "Hindu 'ush" was also found at least in two inscriptions of king Darius ( early sixth Century B.C.), whose empire said to have extended up to the borders of the river Sindhu.
Hindu and Indian are both forms of the original Sanskrit word "Sindhu" meaning river in general and the Indus river in particular. The Greeks referred to those living in the subcontinent as "Indos" while the Muslim scholars called them "Hindus".The Europeans who came to India from the sixteenth century onwards followed the same tradition and referred the natives as Hindus to distinguish them from the non-Muslims.
Hindus never referred themselves as Hindus until modern times. It was only during the 18th and 19th centuries that Hindus started accepting the word.
There are many interesting stories and explanations about the origin of the word 'hindu'. Some modern Hindu scholars believe that it is derived from the sanskrit word 'Hidi'which means to achieve one's objective
More info at http://hinduwebsite.com/hinduintrod2.htm