Is it safe to use a cold wallet like Trezor or Ledger to stake ETH from work computer?

As I keep reading about all of the Coinbase account hacks and the need to move crypto to hardware wallets, I realize I'm doing much of my trading on a work computer. It's all I got. Certain wallets want to use storage on your computer (it's technically not mine) and I'm doing a host of financial transactions on this thing. Does that mean my employer or IT dept has backdoor access to my ethereum? I genuinely have no idea how that works. It's an honest question. Anything I should be concerned about if I decided to get a cold wallet but my only computer device is a work computer?