Let’s assume you are out of work at present, that you will not be moving house for the job as it is a short term contract and that the notice period is 7 days each way. (Often with a contract the notice period is 0 within the firsts 14 days.)
An employer can bring you in for an interview, take up a day (unpaid) of your time, and a day of the time of at least one of their staff, at the end of the interview they don’t truly know how well you can do the work, you also don’t know how well you will get on with the rest of the team.
Or they can bring you in for a week, pay you to do useful work, and be willing to end the contract just paying you for what you have done. If they do end the contract after a short time, you don’t need to show it on your CV, as you where between contracts anyway. (You can also end the contract if you don’t like the work.)
From your CV the employer will know you have done lots of contracts like what they are asking, and therefore will know that other employers have decided to take you on after an interview and not terminate you after the first week. For contract work, the employer is looking for someone that has already used the required skills, rather them someone that can learn, so it not interested in “potential”.
So what have you got to lose…..