Yeah if you are seeing shorts I would put the brick away and order a new one.
They expect the power for the most part to be regulated before entering the laptop circuitry (the reason why they have a brick in the first place) and causing shorts and etc can not mean good things. If you can tape up the wires (the exposed one individually) , you can repair it for a short term fix.
You can fix it, but, again your going to need to cut the wire and shorten it and do a lot of work. It might be cheaper (as in time wasted) to buy a new brick.Since the pic you posted looks like an older dell you can find a bunch of them on Ebay and etc for decent prices.
Also, its not a transformer as its not stepping up or down AC, but its converting AC to DC and providing a constant amount of power.
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