I think you can find a wig at Party City (even order online) for nearly nothing. I do believe a wig can be manipulated in such a way that it can looked shaved without being shaved.

One way to to this is to buy bobby pins that match the wig. If it's a bit off, don't worry, you'll know why in a second. Adjust the wig to your head so it wont come off or loose. Then, with a comb, brush the part of hair you want to "shave". Pull it tight, and then TIGHTLY wrap it around to the other side of the head, letting the wig hair fall over it. Use a non-alcohol based hair spray to flatten it out. And bam, instant side cut.

You can do the same in a different way with another wig (mind you, these wigs from party city are at most $10. Most being cheaper especially now, so maybe considering buy two of the same. AND A WIG CAP THAT MATCHES THE WIG COLOR). Part the wig where you want it to appear shaved. Bring that hair to the side of your head, and leave some behind. with what's left behind, cut. Cut first slowly and in bits. Then once you get to where it would be normally "shaved", cut very short.

I've worn a lot of wigs and own.... we will say a few. They are easily manipulated if you're using synthetic fibers. Which all cheap wigs are.

I hope this helped a bit.