The term "bloodless surgery", in the early to mid 20th century, was used by chiropractors.
Where this term came from was from the practice that was modeled on Dr. Adolph Lorenz's avoidance of invasive surgical methods due to his allergy to carbolic antiseptic. He developed a 'deep massage' technique that allowed him to manipulate a person's internal organs and bones without using conventional surgical procedures. This method was picked up and practiced by those in the chiropractic profession.
George Starr White, a chiropractor whom the WT supported and promoted, also practiced this method of bloodless 'surgery' (manipulation). Another practitioner who followed this method was none other than Felix Kersten, the so-called doctor who treated Heinrich Himmler during WW2 (and, incidentally, Kersten ended up in Switzerland after the war).
How J.W came to the idea to catch up that term "bloodless surgery" or was it "bloodless medicine" is presumeable accidently. (?) because it is not really "bloodless" but "transfusion-less".
The WT has always been pro-chiro and pro-osteopath - in other words, anti-AMA.
It is not surprising that Dr. Major Bertrand DeJarnette dropped the use of the term in the 60s because that is when Dr. Cooley developed a method for doing open heart surgery that required the heart to be free from blood while it was being repaired. Cooley's method was never meant to be used for surgery that could be handled by conventional means - it was the JWs who came up with the brilliant idea to use that same method for surgeries that did not require a bloodless field.
And as far as bloodless surgery being "transfusion-less"...it isn't. The entire field of bloodless surgery is dependent upon transfusion technology - it does involve transfusions. Transfusions of a patient's own blood. What bloodless surgery avoids is donor blood (sort of...a lot of the drugs and products now used in bloodless surgery have blood components in them). Once transfusion technology was advanced enough, that is when 'bloodless' invasive surgery became possible. And that is when the chiropractors dropped the use of the term.