Upon deciding to revisit this gem I realized I can't find a solution to this anywhere.
So, here's my take.

How to install:
1. Verify integrity of your game files.
2. Make sure you're not on beta channel.
3. Get this patch in xdelta format https://www.dropbox.com/s/gejnhvu8ho8qj3h/DISGAEA2_PC_DS_BUTTON_PROMPTS.xdelta?dl=1.
4. Get XDelta patcher (I've used the UI version from here https://www.romhacking.net/utilities/598/).
5. Patch the SUB_DATA.DAT file inside your Disgaea2 PC install folder ("Steam\steamapps\common\Disgaea 2 PC" for me)
6. Replace the original file with the patched one
7. GL, HF

Button icons were taken from here: https://opengameart.org/content/free-controller-prompts-xbox-playstation-switch-pc1.

Preview:
https://www.dropbox.com/s/js38bzbk0fbay3a/20230420144842_1.jpg?dl=0