1. No amount of stretching can replace breaks imo. 5-10 minutes every hour is reasonable and what I try to do. If it's a long session, like 8+ hours, I will try to take a longer, 20-30 minute break in the middle.
2. Regardless of what techniques you are performing, you should not be tensing your arms, hands, or fingers. If you have to tense up in order to multishine, for example, you need to retrain your muscles to relax while multishining. It feels weird, but I have found that my consistency, precision, and speed only increase when I learn to relax my muscles. Pay attention to other players, especially new ones, next time you go to a tournament. Players that look like they're spazzing out on their controller tend to have haphazard control over their character. Players with masterful control will tend to perform inputs with smoothness and fluidity.
3. Pay attention to posture. If you've followed any of Caitlin McGee's stuff (check out her Twitter if you haven't), you'll know posture is important because it's essentially the foundation for everything else. If you lean forward with your forearms pressed against your legs, that alone could be a major contributor to forearm/wrist pain.
4. This is a no-brainer at this point, but document what kinds of pain/sensations you're experiencing and try asking your doctor about them. If you have a condition that makes you particularly vulnerable to hand issues, it might not matter how you take care of them. If your hands are ticking time bombs, it's better to know now than later. I bring this up mainly because your join date is fairly recent, so I imagine you haven't been player for very long. I'm sure you've played other games, so that could be part of the reason, but Melee is much busier than any other game. It's only been in recent years that older players have started to have hand pain at a notable rate, but after just a few months to a year, I wouldn't expect any hand issues unless you have terrible form.
5. Finally, an actual answer to your question.
Here are videos of the stretches I've been using, and I'm really satisfied with the results (I do 20 reps instead of 15 for the stretches in the second video though).
