Do you ever trade at work or trade on your work computer? Any reason why you think this might be a terrible idea?
Maybe some employers legally use devices on network to see what is going on, others might use keystroke capture software or devices - so it is not a good idea to use a third party PC to access your trading account whether at work or anywhere else.
I would stick to using safe laptops or PC in your own home just to be on the safe side.