you can either use the sticky wraps that one gets a the hospital which sticks to itself..so you can wrap as tight or as loose as you need to (there are some ACE bandages that stick to themselves too. ) Or try fine strips of gauze that you can use the little peices of metal to attach them...teeth in the metal bites into the cloth itself, again avoiding using pins, or tape.

It seems to me that in order to conceal the fact that the "missing" arm is in fact only taped to the actor's body, additional costume attention may be needed.  How about putting the actor in a somewhat larger jacket so his body can also be padded out a bit so as to eliminate lumps under the clothing where the hidden arm is?

I'd hate mention any other parts of one's anatomy that might be sacrificed for a role!