There’s no need to change your radiators when you switch.
All that is changing is the heat source. Put simply heating oil is normally used in a ‘wet’ heating system, where an oil-fired boiler heats the water, then provides central heating via radiators and hot water to the taps in your home.
The main difference between gas (mains or portable) and heating oil is that heating oil is delivered by road and stored in an oil tank somewhere outside your home. If you live in an apartment, there may not be enough space to site the tank and so conversion would sadly not be possible.