Yes, you can sew a mask with no iron, no pins, and no sewing machine. Just a needle and thread, scissors, mask kit, and a lot of time. My trial run (photographed below) took a couple hours, giving me plenty of time to catch up on podcasts. I could probably learn to do it faster, but one was enough for me.
To hand sew, more or less follow the instructions here, but knot your thread every time, and avoid any extra stitching. Remember that screen printing stretches and distorts the fabric a little, so the pieces won’t line up perfectly. The important bit is to get those center seams properly aligned. Don’t worry about the rest being wonky, it will all come out OK. I used a simple running stitch:
Notice that I still sewed a little bit inside the print area. It looks better when it’s turned inside-out, trust me.
When I sewed the two faces together, I started at the center seam, which allowed me to skip the pins. Hand sewing is slow and meditative, and allows you to gradually align the fabric as you go, instead of pinning everything before. But you can still use pins if you prefer.
I also skipped the iron, and just finger-pressed. Of course you can still use an iron if you want.
You can skip the top stitching, although my Momz says that without it, the masks sort of puff up in the laundry and have to be re-ironed. I whip-stitched mine after turning it inside out:
Above, you can see the running-stitched nose wire channel.
The result is a perfectly good, very time-consuming mask, and that surprising sense of satisfaction that comes from making something entirely by hand.