Is the wig particularly large or unbalanced? If unbalanced, I'd add counterweight to balance it (it will be much more comfortable that way, too).
I had very short hair at one point and never thought anything of it. I just put the wig on and that was it, never had any problems. In fact, I thought that it was a plus.
Just put it on and see what happens. If you do have problems, then worry about it. You could try a wig cap and clip the wig to that it's a good idea anyway because even short/no hair can get sweat and oils onto the wig.
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan