The primary drawback to running a 240V element on 120V is that the tank's recovery rate roughly doubles. (The 3kW element is only dissipating ~ 1.5kW at half the rated input voltage.)
Replacing a 3kW 240V element with a 3kW 120V element would put you near the amp limits chassis wiring for 14AWG wire, and way over the 15 amp code limit for 14AWG house wiring. If there's a 1500watt 120V element available, it'll be nearly identical to the 3kw 240V unit, and preferable for your setup.
If not, replace it with the same element that you started with (and keep the same fuse.) In short runs 14AWG wiring can take more current, but 15 amps is still the limit for what would actually meet code. It'll be drawing ~13amps, which is already close enough- don't push your luck.