You won't, or shouldn't have a problem with a typical cartridge BB. The left cup doesn't tighten to the face of the BB, but rather to the end of the cartridge, and so can go sub-flush in the shell without issues. On some, even the right cup is without an outer flange allowing you to float the system to either side for optimum chainline.
Assuming the right cup does have a flange, your wider shell will move it to the right by 1mm, so add that to the BBs published spec. for chainline.
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