Is it possible to splice this garage door safety sensor wire with some other wire?
Garage door sensors and buttons are low voltage (usually 24vdc), and low enough current that for the short runs typical in a garage you don't need very large cables. 

18awg "thermostat wire" will work, but you can go even cheaper with 22awg wire, usually sold as "security system" or "central vac" wiring (2 conductor), or telephone station wire (4 conductor - though you only hook up two). 





Also, a little bit of heat shrink tubing goes a long way to making a neat and professional looking splice.