Jason,

Relax. You're just smelling the normal yeasty/fruity smell from an
aromatic wine like Riesling. If the wine is actively fermenting (and
most would use a closed container for whites, BTW) there's little
likelihood of it even absorbing enough O2 to matter. Besides, the yeast
would tend to gobble it up & stop producing alcohol for a bit.

I'm curious though. Why the shaking & stirring?

HTH Mike MTM