If it was me i’d be drilling them out with a electric hand drill, steadily working my way up to 4 / 4.5mm.
I would definately be putting masking tape or some such on each of the drill bits to act as a stop so i couldn’t drill too far. You probably don’t need much more than 5-10mm of the tip of the drill depending on the angle of the drill to remove the bit you want.
I would also be putting some tape round the top tube of the frame so that if the chuck of the drill touches it it doesn’t leve a mark.
As it is a steel frame i am presuming the cable eyelets are also steel so i would want to re-paint them once they are drilled to prevent rusting. Due to this i’d also be thinking about taking the hole out another 0.5mm so i could get some enamel paint on the bare metal and still get the outer through.