The missus is worried about me operating a chain saw, so to put her at ease I promised I would look in to a good pair of gloves to protect my hands, just in case. Are there any gloves out there that are good for saw use? I'm thinking maybe the type like a fisherman's filleting glove.

Not that I know of...
. But I do know what it's like to have a missus who agreed to be my life partner and was depending on me to be around for her for a long, long time. The plan was that we'd grow old together...that carries some hefty responsibilities. Sadly, in my case, my wife died of cancer at age 62.
You have a solemn obligation to her to not bleed to death out in the woods. I'm pretty sure I'm preaching to the choir here, but just stay safe...for both your sakes. Rick