Problem removing dressing. Clothing!

I have average hair of 2cm height on hand not much visible and more on my leg which is clearly visible. Whenever there's a dressing to be done/to remove the bandage after blood test it's very painful to remove it (it gets reddened if removed quick). Like now I have a small dressing of wound on my leg where when I get it replaced with a new one the hair around it sticks and is difficult to remove it even after using the hydrogen peroxide solution on the dressing. So what should be the best possible solution to this. Some say avoid use of the tape and use cream instead but if I don't cover it then it is not safe as even small minute bump on the would result to bleeding moreover the cream easily gets wiped out with clothing