Hmm. That's a good question. I would think if it is bad and your skin is always cracked it might slightly increase your chances. After all, your skin acts a protective barrier against all kinds of stuff. Even little cracks and cuts can let things in, although our bodies can usually fight off most of what gets in.
In order to get HIV from shaking hands, the other person would have to have HIV, they would have to have a cut or something on their hand, and that cut would have to touch yours. So while it might be possible, it is probably not too likely. You could ask your doctor more about it. You could always cover any larger cracks with Band-Aids or liquid Band-Aid. You could also try to avoid shaking hands if it would not make things socially awkward.
As for trying on clothes and shaving, you could ask your doctor about that too. I am not sure about this, but I don't think HIV stays alive to infect another person all that long once it is outside of the body. According to this site dried blood sounds pretty safe:
"HIV is not transmitted through surface contact with dried blood. Incorrect interpretation of conclusions drawn from laboratory studies have unnecessarily alarmed some people. To obtain data on the survival of HIV, laboratory studies have required the use of artificially high concentrations of laboratory-grown virus. Although these unnatural concentrations of HIV can be kept alive for days or even weeks under precisely controlled and limited laboratory conditions, CDC studies have shown that drying of even these high concentrations of HIV reduces the amount of infectious virus by 90 to 99 percent within several hours. Since the HIV concentrations used in laboratory studies are much higher than those actually found in blood or other specimens, drying of HIV-infected human blood or other body fluids reduces the theoretical risk of environmental transmission to essentially zero."
http://ehs.uky.edu/classes/bloodborne/bptr
ain.html