The Cherokee were part of the Indian clearance in the South, but there was also an Indian clearance in the Northern states. Buley covered the big payout in Chicago. The southern clearance was less organized, but payouts occurred.
One of the reason for the Dawes Rolls was to enable the Cherokee, as they organized themselves, to DISQUALIFY what turned out to be 25,000 "others" who appeared to follow them to Oklahoma ~ a large number of whom were grifters intent on stealing Cherokee proceeds from herd and other property sales.
Not everything happened in all places the same way.
The whole idea of moving everyone West was the doing of Thomas Jefferson and the Kickapoo Indians anyway.
Without knowing the germ theory of disease they deduced that Indians living in the presence of whites and blacks were dying at alarming rates so any chance at biological survival required relocation.
You might look up John Metoxen (I believe he's a relative of mine ~ his sister is identified as "Ox In" married to an ancestor). He was a Brotherton, and I suppose technically adopted by the Oneida at the time of the conquest of the Mohicans, and he became quite a challenge to Jefferson and crowd. John advocated removal ~ and all he wanted was Indiana Territory ~ later briefed up to Wisconsin, and for a while he bought into the idea of moving to Oklahoma.
The Cherokee had unfortunately set up shop in an area where Jackson's friends wanted the land. He was less couth than Jefferson.
Still, the folks who walked were the black slaves. The Indians left on horseback and with wagons. In places they actually rode some of the earliest trains in America.
I’m Eastern Band Cherokee and everything I’ve ever read talks about two groups who spent part of the trip on open boats but talks none on trains.
The lady we are descended from was married to a White farmer who was also politically well connected. The 1820 census lists her as Cherokee but the 1830 census lists her, under the same name, married to the same man and 10 years older, as White.
The family story is her husband fixed things for her to stay. He and she also helped groups of Cherokees who were hiding in the mountains.
The Eastern Band is in regular contact with the Oklahoma Cherokees and documentation of the Trail of Tears is pretty extensive including many first person accounts written along the way or shortly after arriving in the wilderness. The Cherokee had a very high literacy rate even back then.