I used to deal with blisters a lot coaching gymnastics and if there is skin on the blister you should keep it there for as long as possible. This gives the skin underneath a chance to toughen up before taking the brunt of day to day life. When our hands were really tough, we'd file down the callouses with sandpaper or emery boards.
If you rip the skin off, you're likely to get sore faster. Once the skin is off, use moisturiser to help the skin recover.

I once saw a kid rip his hand so bad it was bleeding, a lot of skin was taken off. Before I could tell them otherwise, the brains trust at the gym I was at put iodine on it to prevent any infection. The kid nearly jumpeed out of his skin it was so painful.