The publication of many of Boswell's accounts of his life with Samuel Johnson has often been vexed by the number of people who helped Boswell prepare various works for publication.
Most reliable sources conclude that Boswell turned over the completion of the journal for final publication to Edmund Malone, who knew Johnson fairly well but was not a close friend of Boswell's. From most accounts, it appears that Boswell, once Malone was involved in the final editing process, did not spend a significant amount of time or effort on the journal. The day after Malone got involved in the editing, Boswell arranged with Henry Baldwin for the actual printing, and that appears to be the end of Boswell's active involvement in the publication of Journal of a Tour to the Hebrides with Samuel Johnson, 1773.
Although the date of actual publication is uncertain, we have a marked up title page for the first edition of the work indicating that it was "Printed by Henry Baldwin, for Charles Dilly, in the Poultry, [roman numeral] 1785, with a hand-written note at the top of the page from Edmund Malone that it the page looks like an "old one," so it was revised to look more 18thC than 17thC.
This information was gleaned from Pottle, Frederick A. and Charles H. Bennett, eds. Boswell's Journal of a Tour to the Hebrides with Samuel Johnson, 1773. New York: McGraw-Hill, 1962.