I don't know if you can easily (or cheaply) swap the CPU out.
*Also, the COOLER in your laptop is designed for a max heat output. If you get a better CPU (with better GPU) you'll output a lot more heat. It may have issues or be far too loud.
**Also, the BIOS must allow your CPU to be used so the manufacturer has to specifically put the CPU in the list. So it's not just the socket that has to be compatible.
Other:
I'm guessing you don't have dedicated graphics. That means you're using the HD4400 GPU on that CPU. So you'd mainly benefit by having better HD4600 graphics which will help but it's hard to say how much. Plus again, you're likely going to end up with throttling issues due to heat.
If you have a dedicated GPU already then make sure you're using that whilst gaming.
Summary:
I doubt it's possible or at least practical to make a noticeable difference here.