Is the TPS54202 buck converter a good solution to pass the FCC SDoC?
For this power class, it would still be work to use a linear regulator. Indeed, it can get a bit warm, but as long as you have some proper grounding for thermal dissipation, it should be alright. Furthermore, you would not have to worry too much about EMC.

A quick search at TI website gives the following LDO LM317, which delivers at least 500mA if the following condition is fulfilled: $$V_{in}-V_{out} \le 14V$$
which is your case. 

According to the chip's datasheet the maximum power consumption should be around 1.8W:


If you want to increase the noise robustness, you could also add some additional filtering between the battery and the LDO. In order to reduce the common mode noise (mostly high frequency,) a choke-based filter would do the trick.

Concerning the certification itself it is hard to say whether you would pass or not in the first trial without running any pre-tests, since there is an iterative process between measuring the noise, produced either via conduction or emission, and its attenuation via filtering. 

Despite all advice for filtering, my recommendation is to try to avoid creating noise in the first place. That means e.g.:


Avoid creating large loops in your layout through which a lot of current flows. (This might act as a loop antenna in some cases.)
Keep your high speed lines as short as possible.
If possible shield the housing.