Hi there,
I’m not sure if my experience will help much, but my 15-year-old cat recently had a similar kind of wound. His was on his flank, though, and much smaller (about 2.5 x 1.5 cm). Like yours, it just wouldn’t heal; it gradually got bigger and looked quite puffy and swollen. Mind you, just like your cat, he didn't seem to be in any pain—though cats are so stoic that you can never really be sure.
When he examined him, my vet couldn’t say exactly what it was, other than he was certain it wasn’t cancerous. He wasn’t worried about that at all, and I have total confidence in my vet.
He tried a laser treatment session to speed up the healing process, but to get any real results (and even then, it’s not guaranteed), he’d have needed several sessions. However, my cat absolutely hates the vets after a bad experience, so he has to be sedated every time he goes. Because of that, multiple sessions just weren’t an option.
Instead, the vet gave me some honey ointment to apply and I had to put a cone on him. After that, the wound wasn’t really "raw" anymore, but you couldn't say it had properly healed either. Over time, it looked more like a big lump—a sort of messy mix of fur and a half-formed scab. Eventually, after two months in the cone, my cat finally managed to rip it all off and we were right back to square one with the same open wound. After this happened a few more times, the vet finally operated to remove the lesion for good. My cat is 15, so I wasn’t at all easy about the surgery, but I didn't really have a choice in the end. It wasn't fair on him having to wear a cone 24/7, not to mention the risk of it getting worse or getting infected.
Initially, the vet wanted to send it off for histology to find out exactly what it was, but after the operation, he decided it wasn’t necessary. After first mentioning a keloid, he eventually settled on it being a local granuloma caused by over-licking.
Anyway, in my case, it wasn’t anything serious, even though the wound would go back to being raw the second he didn't have his cone on—because, like yours, it just wouldn’t heal and was actually spreading.
This is just my own personal experience, so obviously take it with a pinch of salt.
Also, my cat’s wound was on his side, so it was easy to remove, but in your case, being on the leg and given the size, it seems like it might be impossible without a skin graft.
Anyway, as others have already suggested, it would be a good idea to get a second opinion and see if a biopsy is needed.
Wishing you the best of luck, and give the little lady a big fuss from me!