Removing bullnose from tread in a notched stringer

I'd like to lay hardwood on the stairs that was previously covered in carpet. I plan to use pre-finished flush stair nose ( e.g. ) in combination with pre-finished planks for treads and same for risers. My concern is as follows...
Ideally, for maximum support of the stair nose, I'd like to remove to current bullnose overhang from the pine tread. However, the tread (and riser) is supported via notches in stringers from both sides. They are press fitted, glued and shimmed from the bottom of the stairs. Is it safe and allowed by code to trim the bullnose overhang flush with the stringer? Or am I better off laying the stair nose on the rounded edge?
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