I've recently, successfully and safely achieved what you want to do.
Presuming there is a 'good side' and 'unseen side'. Screw a 6mm piece
of MDF onto the unseen
side, then copy route it, using flush triimer with bearing. Then,
clamp to bench with one third of edge exposed off bench. Then using
roundover bit with bearing, work your way round the piece. If ther are
2 'good' sides to the piece, instead of screws, use tape, acetone
removes all the stickiness and doesn't stain the oak. Piece of cake...