Not really any safety issues other than the quality of the work done. Switching from right to left hand drive will require significant structural modifications to the car (including a LOT of cutting and welding). if you have a QUALIFIED tech to do the job it shouldn't be too bad(expensive though). Just remember you'll need all new steering components (steering column, Intermediate shaft, gearbox/rack, and steering linkages, as well as rerouting all the throttle and brake controls and electronic controls(turn signal, horn, headlights, etc.) Not really a job for the DIY tech, but it CAN be done.
Those cars are very basic, however I'm not sure they made the firewalls symetrical.
I say...Why bother, right hand drive is too cool. People in the USA pay more for vintage cars that are on the right.
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There aren't really any safety issues other then the lack of airbags and the general size of the car. I drive a New MINI, and I would compare it closely to riding a motorcycle, people don't look and they don't see me. So I have to be 10 times more aware. If you have any other questions you can check out NAM if you haven't already. Great people and lots of information!