This is a sleeveless, round-knecked waistcoat/cardigan. Here you can see the two armhole steeks, the steek for the front opening, the 'pouch' where the round of the neck was shaped, and the steek for the sides of the neck.
I cut the armhole steeks one at a time. Before:
I didn't do any sort of basting or machine sewing and that was fine. My big mistake was not casting off the armhole stitches (I held them on a thread as I usually would) and when I cut up the steek they started unravelling! I cobbled them together, but made sure that I cast off the other armhole steek and the neck steek.
Here's the inside after knitting the armband. Still no unravelling!
I have knitted both armbands now and I've cut open the front and neck steeks. I was therefore able to try it on. I was fairly pleased, although the shoulders are a bit wider than I'd have liked and overall it is a bit too big. However, when the neck and front borders are knitted I expect it will shape up a bit better and when I wash and press it I expect it will hang better too.