Hi there,
I would like to offer my expertise on the Web Application development and specifically on Chrome Extensions. After going through the project description here, I understand that you need the urls visitors on your website click (via buttons) to open in private incognito windows.
To do this, we'll need to implement a Chrome extension, which will load on your website. So users will need to install that extension. Without an extension, It's not possible to achieve what you are after.
And I can implement this Chrome extension in about 12-15 hours, so that would be a rough estimate of how much it'll cost you budget and time wise. (12-15 hours * 30 USD).
Also, since this can only be achieved via a chrome extension, I won't be able to give you the source code as such. But I understand your concerns about whether the developer you hire has the right capabilities or not.
If that's a concern for you, maybe we can first discuss the finer details and if after the chat you find my knowledge level and design of this extension trustworthy, you can then go ahead and award the project.
Happy to discuss further
Thank you,
Shamzi