Ok, step by step and drawing for the DIY'er:
Cut off original a/c end.
Strip off a half inch of the black, pull back the wire and twist up nice in order to thread through the hole in the new plug connector.
Strip off a quarter inch of yellow plastic insulation and twist up to thread through other new plug connector hole.
Disassemble new plug by prying in half.
Feed wires through holes in correct leads as shown in drawing and apply rosin core solder.
Crimp in the tabs to hold cord in place.
Put plug halves back together.
Plug in to wall and check voltage with a DMM if you have one, red lead core and black lead shell, if you see 7 VDC you're done!
Plug in to TE and enjoy the fruits of your labor...