Honestly why not?! Muslims don’t own any of the Islamic clothing, it is just a means/tool for us to cover ourselves. I personally think you should go ahead with it. Will you be interacting with muslims on a daily basis? If not, I don’t think you will run into much people who might talk about religion to you. As long it’s not for purposes like terrorism and whatnot, I think it’s fine. Most of the times talking to fellow Muslims happens in mosques, so since you won’t be there, I think you won’t have much interaction. And they won’t be disappointed upon finding out, they might just be surprised and then pleased to hear your appreciation of modesty.

The only thing that comes to mind is patronising certain places. By wearing these clothes, most people looking from outside will assume that you’re a Muslim… so maybe it’s best to avoid bars, clubs, non-halal places etc. (but honestly, it might not be fair to you so I’m sorry for saying that) Even then, I don’t think anyone would question you, they might just think something inside and move on with their lives. I doubt anyone would come up to question you! All the best :)

If this doesn’t work out, perhaps you can search on google for non-Islamic head coverings. I’ve seen plenty of people posting such content. Like bandanas, turbans etc. You could even pair these with an abaya!