It is possible, but. Depending on the severity of your disease, it is possible, but only in consultation with your hematologist. The severity of VWD is quite variable from patient to patient. If you really wanted to get a tattoo, you could pre-treat yourself with the appropriate medicine as if you were having an elective surgery, but you would have to pay for it out of pocket (i doubt insurance would cover it).
Careful. Yes, but you may bleed from each needle injection.