Wall-jumping is not required. If you use it to grab items out of order, certain story beats may play out of order.

Credits:
Testing - The Brothers Crafters#8910, Conner#4315
Zero Mission Hacking Toolkit - Cosmic
Screw Attack damage asm - Raygun
Projectiles continue off-screen asm - Raygun
Intro text OEM guide - somerando(caauyjdp)