Accurate smooth shadows take a bit of time to render, so I was wondering if there was a cheat to do it like how they do in video games, where they add a shadow and then just blur it. If there is and you could tell me how, I’d highly appreciate it!
It sounds like you’re talking about z-depth/buffer shadows. You can use these in Blender Render, but not Cycles (as far as I know).
Some renderers like the old Mental Ray allowed you to mix raytracing with shadow maps, but pretty much any modern renderer is going to be fully raytraced, so the answer is essentially: no. Blurring shadows (by making the lightsource larger) will most likely just add noise and/or increase your render time.
The solution to save render time really depends on what you’re rendering. You could set up lightmaps (also used in many games), but the set up time might not be practical. (Is there animation? What kind of project is this?) You might spend more time (and human hours) setting up lightmaps or switching renders than it would take to let the computer do the work and just render.