Quote " I plan to take out the outer sealant for a few mms with a pick tool and replace it."
In a word,,,,,,,,,DONT.
You will create a bigger problem as new sealant will not stick to old.
If there is a leak the only way of fixing it is to remove the rooflight , clean it and the van of all old sealant and apply new, refit the rooflight.
If it is windy and very wet where you are the water is probably being driven in under the lip of the rooflight.
There was a fix to stop this happening to some extent and that is to get a length of L shaped plastic slightly longer than the width of the rooflight and glue it to the roof in front of the it .
Sealant to use to fix ,,,,,,,Soudall Fixall.