EMI Input Filter Design
The specific application I am designing a filter for is a 24V, 120W
flyback converter in the consumer electronics market.

The very first thing I would do is simulate the circuit in order to understand the current consumption and harmonics in the worst case loading scenario. In other words: -
$$\boxed{\text{Don't try and design any EMC filter values until you have this buttoned-down.}}$$
Then, still using a simulator, I would mimic a feed cable of the appropriate length terminated in a LISN connection so that I can actually get to the noise/interference voltages that might actually be produced by the switcher. LISN example: -

Picture from this website. At this point I have to mention this: -
$$\boxed{\text{The above is an attempt to establish conducted emission values}}$$
Having said that, pretty much most of the radiated emissions are going to be emitted from the feed cable so, it's not such a bad thing to only concentrate on conducted emissions.
Regards the LISN and the feed cable, you will have to decide what the set-up is and, this is determined to a large extent by what conducted emission standard you are trying to meet. I can't tell you what this is so you need to do your homework.
$$\boxed{\text{Decide on the standard and read what LISN it uses}}$$
You will also need to evaluate the feed cable and estimate to what extent it may not be perfectly balanced with respect to earth. You have to do this in order to generate conducted emissions because, if you didn't do this then, in a simulator, because the cable would appear to be &quot;perfect&quot;, there would be zero common-mode conducted emissions and that would be pointless to pursue: -
$$\boxed{\text{So, model your power feed cable with attention to detail}}$$
You actually might need to do some physical testing on a cable to determine how imbalanced it might be relative to earth.
The actual easy bit (that takes very little time if done properly) is adding whatever common mode filters and chokes are needed to reduce the emissions to a reasonable level.
However, do not skimp on modelling the CM chokes at this point; do some research on what resonant frequencies the CM choke may have and thoroughly satisfy yourself that your model is good.

My design (and the reference designs I am using) does not feature any
Y-Caps because the line cord does not have an earth-ground connection
prong.

Well, in that case you have no ideal place to connect the CM mode capacitors and you will always sail close to a pass/fail if you do not take great care reducing the harmonics of current consumed through live and neutral. Even more reason to simulate.
$$\boxed{\text{This is how I would do it}}$$
But, there's no guarantees you will pass your conducted emission test because reality is never the same as a simulation. However, not simulating isn't really a viable option these days because you will definitely significantly improve your chances of getting close to a pass by doing so and, pretty much, all from the comfort of your desk.