The Vox C2 has an FX out* so that can feed the mixer and you should be able to set the speaker level to anything from nowt to mayhem.
Similarly the Marshall, that has an "emulated" output and should again allow silent practice.
For sure the Vox will sound better micc'ed up and running pretty loudly (the bass is probably best DI'ed? Whole thread on that elsewhere!) but running a loudish guitar amp is going to be problematic with live mics? Depends whether you just want a practice set up or a really "nit picky" recording.
And on the theme of K.I.S.Sir, do you really need the mic pre amps? (technically of course you don't. The Yammy's pres are well able).
*I foresee some earth loop issues. Be prepared to snip some signal shields!
Dave.