For cheap? Use the 240V already in the building. Sometimes you find a place with a 240V air conditioner socket (15-20A) already installed. Or if you're comfortable assembling such things buy a sub panel and plug it into the stove or dryer socket (240V 30 or 50A) and install a 15A two pole breaker to give a 240V 60Hz split phase supply to a socket of your choice. Note that in an apartment you sometimes get 2/3 of a 208Y 3 phase supply so you'll have 208V and not 240.
UK/EU devices are designed to work with a power supply that has the neutral bonded to the earth at the installation source. US 240V is split phase and there is no earth-neutral bond in this case. It might be ok, or it might cause problems, ie with the mains input filtering. Proceed with care and caution if you choose to do this.
What hazardous situation do you envision? The power is earth/neutral bonded, heavily, around me with a ground rod every house (I think modern code is 2 per building with #8 wire) and a wire running down every pole, all bonded together, the earth is just connected at the center tap of the pole transformer 240V winding feeding the building instead of one end. In a mains filter the Y caps to earth would see less stress only having 120V across each rather than 240V across one.
The big gotcha that does come to mind now is RCD/GFCI protection on 240V circuits in the US is uncommon, the breakers are available albeit expensive and probably special order for 15A. Also don't trust a non contact voltage probe around split phase, mine (old and cheap) only triggers on split phase cables sporadically, I guess because it's sort of balanced power with no neutral load, so it radiates less?