Not sure whether the discussion has veered into mere non-availability of a body to cremate, rather than the wider subjects of fufilling the deceased's wishes in their entirety, and what needs to be done on a person's death.
Let us re-state what the dead "friend" instructed before his end, in addition to donating his body for dissection and organ-harvesting. "He did not believe in any rituals too and hence his family decided not to perform any rituals from first day."
In other words, he ceased to be a Hindu even before death.
This is no different from situations where someone has turned permanently to atheism as his way of life, converted to Islam or Christianity, or some African voodoo cult, or some Oceanic practices such as those on the Islands of Yap, Borneo, and New Guinea.
Should the survivors still see the deceased as a true Hindu but for his ("overlookable"?) idiosyncracies, and carry on with cremating a "koorcha" or "pillu-kattu", performing anthi-yeshti kramams, such as maasikams, shraaddhams, naandees, daanams, asthi-immersion in Ganga and other fast-flowing sacred rivers, Brahmana-bhojanams, Kaashi, Praayaa, and Gayaa shraaddhams?
Even if they do, with all the bhakthi, shreddhai, vishvaasam, and treasure at their disposal, will his Aathma accept them? Does the deceased even have an Aathma at all? In pithru lokam? Vasu lokam, Rudra lokam, Aadithya lokam? Narakam?
With the utmost respect, the comparison with Bhageeratha bringing down the aakaasha Ganga to purify the asthi of his ancestors and elevating their Aathmas to Deva-lokam, Brahma-lokam, Shiva-lokam, Vaikuntam or other celestial abode is misconceived. These ancestors DID WANT those rites performed. Bhageeratha carried out their wishes. And incidentgally benefitted all of us.
The "friend" under discussion had before death distanced himself from all this "gibberish" (to him). So any rites or rituals can be compared to aahoothis performed on ashes instead of a blazing sacred samith-fire fed with pure cows'-milk ghee and specially-prepared havis (cooked white rice) and other prescribed homa-dravyams. Or can be compared to performing a great music-drama-and-song concert by gifted artistes to an empty theatre or before an audience of completely deaf people.
Let the pitiable man's spirit go where it will, do what it wishes, be what it wants to be; and let us not trouble it with our unwelcome importunities and unwanted, non-understood rituals.
Out of goodness of heart, the surviving family members, if they so wish for their own spiritual welfare, can feed the poor, feed the learned and deserving Brahmins, contribute to erect libraries, schools, hospitals, clinics, shelters, temples, and to renovate, improve, expand, and endow those already erected. They can found bursaries, awards and scholarships to uplift the downtrodden by society, institute travel grants to students to widen their perspectives, to establish contacts and return to serve the country better. They can even made donations for public projects such as roads, bridges, railways. public parks and gardens, water and power supplies.
s Narayanaswamy Iyer