The question is, how can I prevent the glue squeezeout from ruining
the
look of the joint? Obviously sanding after glue-up is not an option
because of the stain -- I need some advice on how to get rid of the
squeezeout without marring either the stained edge or the delicate
plywood on the other side of the joint. Any thoughts you have would
be
much appreciated!

I don't see how this could ever work. No matter how good your glue up
of the edge, it won't be perfect, and you will need to sand the top of
the table.

I agree with the other poster in using a darker wood for the edging.

You know that walnut is going to lighten considerably over time?