Can you buy cross bikes designed for women? I'm only 5'3" so mens' bikes never fit...
There are small differences in the build of men and women. Basically the ratio of the leg length to body length is different but the differences are relatively small. And many women have the same short leg - long torso build as men and many men have the long leg - short torso identified as female.
The problem isn't that you're a woman but that you're a small person.
At 5'3" you are probably looking at riding a 50 cm road bike. That would imply that a cyclocross bike in your size would be at least a 48 and perhaps a 46. Basically look for a cross bike in which you have about 2" of standover clearance and a "reach" (top tube length plus seat setback if any and stem length) about 1-2" shorter than your road bike assuming you ride road a lot and know what this length is. Otherwise you can estimate this length by trying to assume the position on the bike with your upper body at 60-70 degrees (leaned forward 20-30 degrees) but with a lot less weight on your hands and arms than would be the case with a road bike.
I would suggest looking that the "compact design" Giants and so forth.