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.
When you are applying to a company it is important to know and understand all of the rules and how they treat their employees so you can have an idea if it is advisable to do trading at your office. Most of the companies are not that strict that they monitor every small activity of their employees so I think it is good to trade at work but to make sure you are safe, just bring a pocket wifi and a decent laptop so you will not get monitored.