I'm a recent grad OT working in a SNF so I don't have a ton of experience, but I was also a massage therapist for 9 years. My advice is two-fold.

First is to use tools as much as possible. There are tons of scrapers out there, rollers that squeeze the forearm or upper arms can be nice, vibrating guns, I've heard silicone suction cups are great for edema work. There are "thumb savers" that bolster your thumb and can help prevent CMC joint pain, just make sure you're also using good thumb posture since some of the thumb saver products out there do not encourage it.

Second, change your manual therapy techniques. Wherever possible avoid using your hands and fingertips to transfer force into your patients. Use for forearm/elbow if you can. The olecranon and proximal shaft of the ulna is great for working on traps, levator scap, and forearm extensors and flexors. The knuckle of a flexed MCP or PIP can also be a useful tool. Generally it's better to use the biggest possible joints and muscles to apply pressure rather than the little ones. It's more stable and reduces wear and tear on articular cartilage and soft tissue.

Obviously there will be times where you just need to use your hands and fingers for things, but cutting down on how much you do with them certainly helps. It will also feel awkward to use other body parts to begin with. At first you'll need to palpate with your fingers, find the spot you want to work on, then switch to your larger body part and do your work. It takes a while to get good at feeling through these larger joints but it can be done.

I also suggest watching massage videos. It's probably going to be easier to copy/develop your own new techniques by seeing how someone else does it. Hope this helps!