In this case it's not really a question of technical possibilities, but corporate policy: if it says you can't install any software without permission, then better don't try as it can be used against you. If there is no such clause in your contract, there is no much difference between downloading and using Portable Apps Platform software (which is mostly open source, but beware of catches such as IrfanView which is free as in beer only for non-commercial use) and bringing your own copy of Paint (on a pendrive, for example).