Either works.
Even if your mon was illegal, unless it is super illegal, you won't get obliterated by HOME or Bank. They got terrible hackchecks.
However, for the sake of discussion, I'll be continuing with a 'strictly completely legal and correct' mindset.
For the record, for most mons, the met date of a mon don't truly matter; they could be met at any date due to the fact you can change your NDS/3DS to a large date range.
So they just need to caught within the date range. Going by your example.
Suicune received on 31/01/2022 Gen 4.
Suicune -> Gen 5 (via Relocator) -> Met date changes to 02/01/2022 [Met Date changes with Relocator/Poke Transfer]
I will recommend against using cheats. A lot of games have PID correlations for the mons. While Gen 5 isn't one of them, there's a weird quirk with the PID having to end with odd/even due to OT Gender or something, and the cheats tend to ignore that.
The 'shiny rate 100%' for 3DS games we have is probably a better option, just don't use it with wonder cards.
As long as your trainer name and nickname don't have weird characters, that would be a purely optimal option. Tools > Data > Dump Boxes in the Gen 4 save, then Tools > Data > Load Boxes in the Gen 5 save.
If I'm not mistaken PKHeX should do it for you. If it doesn't, then yeah remove those items with batch editor.
Do note that some forms are dependent on items, so check through all your mons after that.
Same thing, just trade the mon into another save, and change the Species. The key difference in Gen 6 and up is you need to fill in the field Latest (Not OT) Handling Trainer.
If this field is empty, this mon hasn't been traded.
Also, I don't think I've answered anything pertaining to Gen 8?