I would get some light weight fusible interfacing actually, I'd get a small amount of a woven, non- woven & a knit. Cut one of the arms out and do a test to see if the shirt will take the heat needed to fuse.
If that doesn't work, you can try cutting a muslin square the same size as the shirt square, hand baste (like hand basting a quilt sandwich), then treat the 2 fabric pieces as one.