I am not a sparky however I have the annual task of sorting out 800 external low voltage lights every Xmas.
I run each set of 200 via independent transformers.
I would probably avoid tapping into the outside light as your transformer "if required) would be outside.
If it was me I would probably hook my transformer up to an inside socket and run some low voltage wires to your fairy lights, providing they are not a hundred miles away.
Please do not sue me if you electrocute yourself.