GodMode9i cannot write to NAND so it won't be able to write it to SysNAND. Assuming you have the file from your old DSi, you can either use
hiyaCFW and simply replace the file on the SD card or edit a NAND backup from the new DSi to use the file from the old one and
restore the edited backup. hiya being the much safer of the two options.
iirc it's also possible to put the 0000 on a 3DS's TWLNAND and it'll read in the 3DS Sound app which actually lets you copy to SD, I've tried to do the conversion on PC but was never able to get it working right. It's apparently some kinda ADPCM but it doesn't sound quite right in any of the ADPCM variants ffmpeg supports.
Edit: Found my old testing on Discord, in ffmpeg these formats all sound kinda close, but nothing sounds correct:
adpcm_aica, adpcm_ima_apc, adpcm_ima_ssi, adpcm_ct, adpcm_ima_apm, adpcm_ima_ws, adpcm_ima_alp, adpcm_ima_oki, adpcm_yamaha
Correct: (Transferred to SD using 3DS Sound)
https://cdn.discordapp.com/attachments/286686210225864725/930427975378305024/V00041.m4a
VOX ADPCM at 16000 Hz in Audacity iirc: (all of the above sounded similar, this is just from a much older attempt at converting it when I tried Audacity)
https://cdn.discordapp.com/attachme...448907345980/voice01210426190341000410001.mp3 (Warning: Loud)
(Note: I think on GBATEK somewhere it mentions the correct frequency and it's not quite 16 kHz, even at the correct frequency nothing was quite right however)