Source Code for strcpy and strcat
The Arduino IDE doesn't ship with the source/assembly for a lot of the core functionality. It comes pre-compiled in object/library files.

However, you could download the source code for AVR Libc from this site:


http://www.nongnu.org/avr-libc


Obviously there's no guarantee that the files you download will exactly match what comes with the Arduino IDE, but it's useful if you're interested in how they're implemented.

When you've downloaded and extracted the source code, look in the libc/string folder. you should find assembly files called strcat.S and strcpy.S.

As jfpoilpret says in the comments, attempting to modify core library functions is generally not a good idea. They may be getting called by other parts of the core, so any changes you make could break something else.