Whether your hands ache from punching or holding pads, you should massage and stretch your hands throughout the day. Everyone at POW! Gym Chicago can understand how easy it is to injure your hands while boxing, kickboxing, holding muay thai pads or simple conditioning with kettlebells. If you also do manual labor or typing all day, it is common for your hands to cramp and experience onset muscle soreness just like your legs. I massage my hands a lot throughout the day. I do not realize I am even doing it most of the time because I have been doing for so many years. This includes simple stretches as well.
Below is also a video from Mark Rosenberg, D.C.that is a little dated in its look, but it covers the basics. The goal would be to do some combination of these stretches for 2-3 minutes a few times during the day.