Add a url parameter to only one of the two urls

[iprentzas]

Hello everyone,
I would like to know if there is a solution provided by wraith out of the box for that.
In the project I am working in in, everything is pushed into a single url. All the changes that we want to test are being placed in the page with the form of the cookie. Here is how the domains usually look like.

example:

domains:
    current:  http://www.mysite.com
    new:       http://www.mysite.com/?draft=some-cookie

The problem is that if I use it like this, the pages will fail cause from paths, the new url will be:
http://www.mysite.com/?draft=some-bookie/page-url

What I would like to know is that, is there any way from wraith in which I can add the parameter to only the new url?