the cpu doesn't cover the cpu fully? huh? I assume you mean heatplate on the cooler.
if there is a little excess paste you can remove it with a lint free cloth or coffee filter. just wipe it away.
if the heatplate is a tad small, the core is in the center and that is where the heat will be. any excess can be left or cleaned.
Be sure to ground yourself working in your pc, touch case or power supply (bare metal) and then wipe any excess