I'd like to say that I play my Widow all the time. She's all I play. However I believe that they should be able to use weapons other than Arachnos Widow Claws on other costume slots other than the first slot. I believe that the first slot shouldn't have an option because the whole outfit is Arachnos themed, but, since the first costume mission says you need an outfit that is less Arachnos, I think you should be able to swap claws, since I think ARACHNOS WIDOW Claws are a little bit of a dead give away. I also think that with some gloves such as the Ascended Radiance gloves, the Arachnos Widow Claws do not fit very well, and claws like the Vanguard Claws would look much better. That's my two cents on this issue.
I have a question about it though, are you wearing a mask under the hood?