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

Probably not, an iron on patch requires heat and pressure to make it stick. You get both from the iron.

Your steamer may not generate enough heat to activate the glue and it does not apply any type of pressure to the patch. Additionally, the moisture from the steam may prevent the adhesive from sticking to the clothing. The glue would be water proof once it is set, but not necessarily so while it is being applied. Plus the steam will make the clothing damp, which could also prevent the glue from sticking.

You can try it if you like, you just need something to apply pressure to the patch once you’ve heated it with the steamer.