Swapping CPUs in laptops is touchy unless you can find online someone that did it to your exact model and can verify that it worked, or the service manual lists the CPU as compatible. Even if the CPU fits the socket does not mean it will work on the motherboard. So do a web search see what you can find, if nothing, buy the CPU, cross your fingers, do a BIOS update if one is available and try it.
For about a 7 year old CPU, so system is about that old, I would replace the hard drive with a solid state and add more RAM before I touch anything else.