It might fit under the arm if it's really short. Looks like a traveling size iron, but it doesn't show how far out that metal side cord part goes. Nor does it show the cord at all which condition would mean everything. Interesting Singer did make some vintage irons though, but it wouldn't be something I'd pursue even if I were a completionist
My other concern beside cord condition would be the metal against paintwork, it would need to be cushioned which would add size vs. space.