Is it possible to carefully select each item in each area of Lush Jungle in order to avoid battling the other Pokémon?
Yes. You will want to choose the following items to avoid fighting extra Pokemon:
The Mago Berry under the tree to the west, which has only a sour smell. The Honey from the bush in the southwest, with few flowers. The Sudowoodo-like tree in the southeast, which does not have a description about it moving or watching the player. Additionally, this tree is slightly different from the real Sudowoodo due to having leafy branches and roots instead of legs.
Lush Jungle (Bulbapedia)