When on a B&W nightschool course with no home darkroom I stored my stock of paper in a papersafe which I transported every week to the course. When it was at home it was in normal daylight. No problem over a period of 10 weeks

I later converted a room in the house to a darkroom and kept RA4 in papersafes in the room in normal daylight. No problem resulted

Frankly if it hasn't allowed light in in a matter of hours then it isn't going to let light enter in a matter of months

If you have a properly constructed papersafe then I wouldn't worry