I've seen something similar done with that kind of soldering gun to improvise a surface-mount IC desoldering tool that heats all the pins at once.
Pretty clever. The materials won't cost anything, worth a shot assuming it doesn't fry the soldering gun, which I doubt.
I've been reading up these hot wire cutters and any I could afford sound cheap and fragile, if they even work after one use. This looks clumsy to us but it would be quicker melting the foam and last longer (I would think). I gave my grandson an old Weller, maybe I'll snatch it back and try this. IF I do and it works I'll post.
I'm not sure which hot wire cutters you're talking about, but I have the Woodland Scenics one and while it does look fragile, in my experience it's really not.