Welcome, Jane!
I, too, was kind of confused/conflicted about curd cutting at first. Then I realized that people have been doing this for centuries and making fabulous cheese, so I was probably making more of it than I needed to.
Once I am stirring the curd (usually with my hand - well-washed, of course), I cut the bigger pieces up. It works fine.
I also use a bread knife for cutting my curd. I really need to find something just a bit longer, though.