Using a router

I have some pine 4 panel doors i bought from Bnq (argghh) now i want to fit glass panels in the upper panel areas. Took the old wooden panels out and realised, the beading isn't actual separate beading but part of the timber frame! So in order to fit the glass, unless i completely dissasemble the bonded frame i have one choice. To somehow remove the beading back flush to the door frame, so i can fit glass and the bond/nail in new mitred beading.
Question, do i use a router, would this be the best tool for the job, and how, would i set it up? Could of g clamps and straight edge? My main concern is i don't over cut into the fram of course, i need to be pretty tidy.
TIA
K
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