Most tyre places will be able to repair that by the sounds of it Martin.
They basically drill a hole in the tyre where the screw was. Then fit a repair patch that has a stalk of rubber on it through the hole from the inside of the tyre and glue it into place.
I haven't had one done for absolutely years and it was under £10 then.
As for safety, I wouldn't think this service would be available unless it was proven to be safe.
At the end of the day it's what you feel happiest about where your family is concerned.