No, I think it will be fine. You worry too much :-) I'm just giving you a data point to tell you that you don't need/want your curds to be that firm for when you cut them. Curds at the beginning are always very fragile and they will shatter if you aren't careful with them. As they cook, they firm up and at some point (usually around 20 minutes of cooking in for me), they are pretty robust. If you are using raw milk, they tend to be firmer, but they are still fragile. If you are using homogenised milk... they shatter if you look at them funny (still haven't made what I would consider a good hard cheese with homogenised milk...).
But when you cut, you should wait between 5-10 minutes after cutting for the curds to heal. Then when you stir, you shouldn't go round and round. Instead, just take a slotted spoon and slowly lift the curds from the bottom of the pot to the top. Cut any curds that are too big. Spend a good 2-3 seconds doing that. Then do it again in another place. If they are shattering, then give them a minute to heal some more and try again. All you want to do at the beginning is to move the curds very slowly and stop them from matting together. Later you will stir more vigorously to get them to expel whey.
It just depends on the milk, though. With raw milk it seems you can be quite vigorous at the beginning (I've never had a chance to use it), but with pasteurised milk, you have to be careful. With homogenised milk, you practically have to stir it once ever 2 minutes or so... it's very annoying.
But like I said, don't worry about it. Cheese making is very, very deep. You won't make the best possible cheese right away. Even a couple of hundred cheeses in, you'll probably be puzzling things out. Enjoy the journey, not the destination :-)
