Tell them a week of working doesn't offer any experience at all, that is the stupidest thing I've ever heard. Any legitimate job that you would actually learn from takes at least a week just for training. Anything you can start right away and just do for a week will be mindless busy work that will teach you nothing. Your school blows.
If you're looking for an internahip with a ski production company a week its unlikely to happen. The big ones arent interested in short term as there is little prospect for them and they only really consider applications through a formal application for a vacancy, the smaller ones are either too small to feel like they can take an intern on or aren't doing enough in a week for it to be worth the trip. If you are interested in ski production i would reccommend looking to see if a company making fibreglass boat hulls or aircraft parts woul take you on for a week as its probably the most applicable production method to ski building available in the uk. Or you can try and get a placement in a ski shop workshop.
I have a similar interest, I'm currently studying design engineering at university and as a part of my course my entire third year (40 weeks) is spent as "a year in industry" I'd love to spend that year working for a ski company, being involved in the design and build process of skis. If anyone knows where to start looking for this aside form just emailling a bunch of ski co's please let me know!