Just rinse the cartridge in water taken from your tank or water treated with dechlorinator. Only replace cartridges if you absolutely have to otherwise you will crash your cycle. It looks like you worked that out for yourself.
I have a filter that takes cartridges and it holds 2 cartridges, so if you need to change, then only change 1 at a time. Is yours similar?
If you do have to change a cartridge then some bottled bacteria might help. I like Dr Tims One and Only.
Do you know what the make/model of your filter is? I might be able to point you in the direction of an adaptation thats better than using filter cartridges.