Thanks, everybody, for your replies! I appreciate it.
I just heard back from a vet I trust at the teaching hospital and she said she always recommends older cats, whether diabetic or not, get any new skin lumps and bumps checked, and she said it should be simple enough for a regular vet out by me to do. So I'm finally taking my girl tomorrow morning to get checked. It sounds pretty common for skin tags and lipoma to form, and she said they usually don't do anything for them unless they start bleeding, get infected, or inhibit mobility. I'm just nervous about what if the vet will want to do fine needle aspiration. She told me it doesn't do anything bad but I'm worried just because many years ago, my mom had a very thorough workup done so she could get open heart surgery, and was found to be in great health except for her heart. Then what do you know, three months after the surgery, she's diagnosed with metastatic lung cancer. So that's why I worry about cutting or opening up stuff because are we really sure that doesn't cause the cancer to spread? I'm hoping the vet can tell enough by just looking and feeling. From what I've read, aspiration results can sometimes be wrong too depending on the cells it pulls. I'll be doing more research on it for sure before we go tomorrow morning.