overdrive button relocation

i have a 98, v6 3.8l,automatic.I just installed a new shift knob,but am having trouble figuring out how to relocate the o/d button.i have the new bracket for it but i cant figure how to get the button out of the old handle.Could i cut the wires,pull the button out and install in the new bracket?If i do that and reconnect the wires with connectors,will it still work right or will i have screwed myself?

Any help or suggestions would be much appreciated.