way to overthink it Wolfgang. ;)
And thanks for stating the obvious regarding the ID of (cheap and readily available) brake outer. :roll:
In the case of a 7speed kids bike any unwanted compression from using brake outer is irellevent as:
The only tension in the “system” is from a puny spring in the rear mech
Being a 7 speed system the outer doesn’t need to be completely compressionless for tolerances to be perfectly adequate to “index” perfectly. (Gear outer isn’t entirely compressionless either BTW)
Braking forces (far greater) don’t cause brake outer any major detrimental problems with outer cable compression.
Yes, it’s a bodge and I wouldn’t dream of suggesting otherwise. Many others here are suggesting “bodging” the use of XT or XTR shifters and mechs. Which I might point out (unless you have access to a time machine) will be indexed to 8 speed at best.
8 speed and 7 speed do not even share the same cassette sprocket spacing. 7 speed sprockets being 5mm apart, 8 speed being 4.8mm (that’s 1.2mm difference in indexing across the cassette). Yes, it’s do-able but not exactly ideal.
I normally stay away from here for a reason.
Di2 it is.