Even though you've got a 10 gallon tank, theres a lot to be said for keeping a small sponge filter in the corner for this very reason.
I keep 2 HOB
power filters on my 46g tank. When I change a cartridge on 1 filter, Ive still got the other power filter with an established cartridge. I wait 2 weeks, then change the other one, if I have to.
However in your case, it would be best to leave part of the OLD cartridge (cut a square of the fiber media and place it with the new cartridge). That will definitely help. You're subsequently trying to avoid a mini-cycle.
46 Gallon Bow F/W: 4 - Zebra Danio's, 2 - Red Platy's, 2 - lg. Silver Dollars, 1 - Pleco (4.5"), 1- Gourami, 1 - Cory Cat, 1 - mystery snail, 4 - Cherry Barbs, 1 - Black Molly