If you switch to an m-unit, you want to re-wire (as you plan). The m-button is nice, but unnecessary. All the wires coming from your stock handlebar controls (if you want to keep them) run straight to the m-unit. You can essentially eliminate all wiring into the headlight bucket except for the H4 plug.
I buy and use wiring from McMaster. It's 18AWG for current carrying circuits, and I use 22awg for control circuits. It's cheaper and easier.
You still need your starter solenoid, but you can eliminate the starter safety motor as its already internal to the m-unit. Plus the Winker relay.
Your stock key switch can be reduced to only a RED wire and the BLACK. Brown and BR/WHT go bye-bye.
From your controls, wire runs straight to left side of m-unit. Output from m-unit right side is all
switched 12v so that wiring goes straight to the component its controlling (brake light, headlight, turns, etc...). Super simple.
You do not need a momentary button to control the m-unit. This is only during setup, and a simple ground jumper wire is the DIY workaround.
I run all my wires inside plastic braided sleeving instead of solid sheathing for simplicity. Some heat shrink, solder, and decent crumpets and you're good to go.
What you waiting on?