How short is short? You can definitely have options, even with super duper short hair! The only thing you have to make sure is that whatever length veil you get isn't heavy enough that the comb will fall out of your hair. If you want a long veil and a combed one won't stay, then consider maybe a mantilla (lays on top of the head and is secured by a bobby pin or two.
I have posted these pics many times, but will copy/paste them again just so you see some options:
Here are some "extremely short hair" cuts, mostly pixie cuts.... if your hair is longer than that let me know and I'll post some pictures that better show your hair length! :)
If your hair isn't pixie short, here's a few more: