The use of for and by in this case are virtually interchangeable although the meanings are slightly different. "For" relates to how long something is going to happen (The duration). Whilst; By relates to the "deadline" for completion.
For = Duration and By = Deadline
"I wanted to delay this meeting for two days".
We use for with a period of time to refer to duration (how long something lasts): Ref C.E.D.
We use "by" meaning ‘not later than’ to refer to arrangements and deadlines: Ref C.E.D.
"I wanted to delay this meeting by two days".
Meaning The meeting is delayed for two days at the most.
Also is it correct to say "delay something until two days later"
Basically yes though this add-on is not specific
"I want to delay this meeting until the day after tomorrow"
"I want to delay the meeting, until after the weekend".