For example, I trade a shiny Kantonian Sandshrew for an Alolan Sandshrew, will that be shiny?
If you’re talking about the ingame trades, no. The ingame trades for Alolan variants in LGPE do, however, have a 1/4096 chance of being shiny, regardless of whether the Pokémon traded is shiny or not, so you can hunt them if you want.