I appreciate the idea of reusing the breast pump sort of goes against natural instincts but it is fine.
From THE WOMANLY ART OF BREASTFEEDING, La Leche League International, Sixth Edition, p. 158-159, 161-162.
"New research has shown that human milk can safely be kept at room temperature (66-72 degrees F) for up to ten hours because of its remarkable ability to retard the growth of bacteria. Milk can be kept refrigerated for eight days."
Lots of working mums pumping during a work day 'wet store' their pumps and reuse them and they don't have access to such a great fridge. I say wash your hands and go for it. I would probably store in a separate container though as PP says. These cooled batches can later be combined for a feeding or for freezing.
And a massive congratulations and well done for deciding to follow your mommy instinct and postpone weaning.