I was mostly just worried about the sewing part, and deservedly so, as I can't seem to sew in a straight line with the machine, particularly with bumpy, stretchy fabric like this.
In fact, when I did cut it, I did cut through some of the reinforcing threads (by cutting perfectly straight through crooked sewing), so I ended up going over that part with an overcast stitch afterwards. I was hoping the wool would be grippy enough that I wouldn't have to worry about it, but it isn't quite (two ends tried to come loose while I was picking up button-band stitches, though it was easy to catch them and set them back in), so I feel a lot better about it having gone over them again with the machine.
Other than that, the cutting itself is easy-peasy. Reasoning that the worst thing I could do is somehow cut through both layers, I grabbed a small bit of cork board I had laying around, and put it between the layers to prevent that. I don't know how likely it ever was that I'd actually cut through both, but once it occurred to me, it seemed foolish not to take precautions!
It seems to me that cutting armhole steeks would be about the same level of nerve-wracking as cutting open button-holes; you wouldn't want them too big by mistake, so just take precautions like you would for button-holes. In this case, I only had to cut open the front, which is more about keeping straight with your sewing and cutting.
Delighted with the button-band so far, and with how neat the pressing made the edges!
Of course, once I reached this point, the mail arrived. Now I'll have to put the Oranje down for a little while so I can get my work done, but being so close to done, it should be easy to get myself to pick it up again soon.