Below is a link on Google Books to 'Public Documents Printed by Order of the Senate of the United States...', 1844. I found it somewhat easier to follow by selecting "Order by Pages" though it is not in chronological order.

Page 95 was written in Dec 21, 1844 by the Committee of the Treaty Party calling the trial a "mockery of trial by jury".

Page 114 (begins on Page 113) was written from Tahlequah on Dec 31, 1844 by the judge who presided at the trial, David Carter. I presume Carter's letter was prompted by the above complaints of the Committee of the Treaty Party.

Pages 120-123 begin with a letter from Brig Gen Zachary Taylor to "Judge Hicks or the Presiding Judge of Saline District". The response comes from the presiding judge, David Carter, and is addressed from Grand Saline.

There is nothing specific as to where the execution took place but Judge Carter's letter addressed from Grand Saline would seem to indicate the trial was at or near Grand Saline (now Salina) and I would presume the execution was carried out there.