Unfortunately in terms of raiding someone and sending your audience to a website at the end of your live stream is not possible through Twitch, you can only raid other live channels currently on Twitch.
One way to be able to send your audience to a specific website if that is what you want to do is to tell your audience you are raiding but you are raiding a little differently, explain where you will be raiding, and put the URL of the website you wish to send your audience to and allow them to click that and go there themselves if they wish to. Obviously, if it was some kind of site that is against Twitch's Terms of Service the streamer themselves could get into trouble with Twitch but as long as it's all above board, you will be fine.
I can understand why Twitch would only allow someone on their platform to be raided as that prevents any problems that they have no control over if it is away from their platform.