"非急需施行的手术" can be translated into English as "non-urgent surgical procedure" or "elective surgery".
"Non-urgent surgical procedure" directly conveys the idea that the surgery is not urgent or does not require immediate attention.
"Elective surgery" is a more common medical term referring to a surgical procedure that is planned in advance and is not an emergency, which aligns well with the concept of "非急需施行的手术".
Both expressions are appropriate, and the choice between them may depend on the specific context and the intended audience.