How close can I trim seam allowances on a head?

I'm going to machine-sew the headcover on my fursuit head, and I will ladder-stitch the two halves together (and the neck) as I glue them on.
I'll leave a good amount of seam allowance, then trim it down so there aren't any visible ridges. How close can I trim them down without damaging the stitches (and yet trim enough so that there aren't any ridges)?
It's kind of an obvious question, but I am inept when it comes to sewing.

Thank you for answering my question.