Steve Elliott
The reason for preferring quarter sawn stock for drawer sides is the smaller amount of wood movement due to seasonal changes in moisture content. For the shallow drawers you are planning I doubt seasonal changes will even be noticeable.

For some reason I just don't like the combination of satinwood and oak. I'd go for maple drawer sides and possibly look for quarter sawn stock if I really wanted to be particular. I'm not sure just why satinwood and oak seem to clash for me. Partly it's a matter of the type of furniture I associate with each species and the historical era they were used in, and partly it's the appearance of the two species that just don't go together, at least to my eye.