Can you use a handheld steamer instead of an iron to attach a patch to clothing?

Nope. That is both moist heat and not enough heat.

Won't work. You need the heat AND the weight of the iron.

No. In fact I've discovered from experience, if you have one of those Teflon scorch preventing covers on your iron, the patch won't stick, either.

No, you shouldn't use steam when attaching a patch. If you don't have an iron, you could probably use the bottom of a hot pan. Just make sure there's a clean cotton cloth between the pan and the patch. Otherwise, if you have a needle and thread I would just stitch it on.

No, you need to press to attach it.

No, you need the weight of an iron, combined with the heat, to make it stick

No. Most instructions for ironing on a patch say not to use steam,

You don’t want moisture, you want heat,

No. It does not get hot enough.