For Wheeler's delayed choice experiment, the 'choice' of a photon is said to be delayed from the reference frame of the experimenter.
There are a couple of things to point out here. First the delayed 'choice' is not an actual thing (e.g. the photon doesn't go backwards in time through the slit and make a different choice), it arises from a common misconception of what a photon is (I'll clarify this below). Second, the reference frame of a photon is not a valid reference frame to take so your Idea Two isn't valid.
So a reference frame is a frame in which we can do experiments, e.g. measure time, speed, length etc. Time is measured by movement of photons or particles (e.g. atoms) relative to each other. The simplest version of this might be the light clock (light bouncing between two mirrors). Observing a single photon there is nothing to calculate time with, it can't 'see' or do anything so it doesn't 'perceive' an instantaneous trip from where it is emitted to where it is absorbed. Further matter cannot be accelerated to the speed of light (it requires more and more energy the closer you get) so a valid reference frame (e.g. containing matter) can never travel at this speed or experience this instantaneous travel.
For more on this see the question "Frame of reference of the photon" (you may have to follow a few links to get the full picture).
For Wheeler's Delayed Choice experiment we can force the photon in the double slit experiment to behave like a particle (by using telescopes at the right distances to detect the photons) or like a wave (by using a detection screen). This results in either two bright spots (the photon only traveled through one slit) or the interference pattern (the photon traveled through both slits and interfered with itself).
Wheeler's experiment was to try and swap the telescopes for the detection screen after the photon had traveled through the slits (or vice versa). Conceptually the photon has now traveled through both slits and is ready to create an interference pattern but then finds the telescopes so has to retroactively go back and only take one slit. Hence the 'choice' refers to the photon's choice to travel as a particle through one slit only or as a wave through both slits. The 'delayed' part refers to the fact that it has to make this choice after it's traveled through the slits. Wheeler didn't agree with the retroactive explanation (that the photon travels backwards through time and changes it's behaviour).
I think the best way to understand (conceptually) the double slit experiments and Wheeler's delayed choice experiment is to forget about a photon as being a particle and instead consider it a wave (see this video for an analogy in water). At any point we place a detector then the wave knocks off an electron at a single point on the dector (e.g. acts like a particle) but anywhere in-between it is travelling as a spread out wave. The interference patterns created by the wave (e.g. the peaks) give the probability of where the photon will be detected.
So for Wheeler's delayed choice experiment the "wave" travels through both slits, it then hits either the detector screen OR the two telescopes (it doesn't matter which or how often they were swapped) and then due to some criteria/interaction with the detector (screen or telescope) it knocks a single electron off. If you think of it this way the photon doesn't have to decide which slit to travel through (it always travels through both), there is no retro-active decisions being made BUT we have pushed our unknown out to what happens at the detector (e.g. what causes the collapse of the wave to be detected at one location rather than at another).
Also have a read of this easy to understand answer regarding photons traveling through the slits.