I was in your situation when I first got my tank and had to do a fish in cycle. Ultimately I decided to upgrade my filter to a different model - but if you decide to keep the stingray here is what I did.
As I didn't want to keep paying for cartridges I bought a box of floss media and stuffed that in where the cartridges were. When you remove the cartridges - you will get an ammonia spike as the zeolite is no longer in there taking out ammonia. To prevent the ammonia spike harming my fish I used API - ammo-lock.
Now you are in a fish in cycle with the ammo-lock acting as a buffer against ammonia spikes - so you need to keep a very close eye on ammonia and nitrite levels - daily water changes are required. Took me about 5 weeks until I was fully cycled. My wife thought I was totally mad doing the water changes every day.
You will definitely want to get an API master liquid test kit as you will be doing a lot of tests and the strips are not only expensive - but not very reliable.
Good luck!
Well I couldn't get the API one, so got the Nutrafin master kit which has 7 chemicals 1 for ph, 2 for nitrite, 3 for nitrate, and 1 for ammonia.
Latest readings are

ph - 8 : definately better than the strips, i just couldn't tell!
Ammonia - Clear - got to be 0 which is the same as the strips...
Nitrite - Slight pink tinge to the water - Strips show no change so close to 0 I'd say
Nitrate - about 40
Which is pretty much the same as yesterday without any change since the tank was moved to our house - 3 days.
About the Stingray.... the cartridges in there are probably months old and I thought this meant that they are serving no purpose anymore, but
after your post I'm not so sure..... can you please clarify about the ammonia you mentioned?
The only other thing to note is that we put in some plastic stuff yesterday (ornaments
probably but wondered if this is normal.... can we minimise it, eliminate it ? What's the best way to do this ?
The only other thing that slightly concerns me is the reading of the Nitrite sample..... Am I supposed to try to match the colour, or the opaqeness of the
sample ? The colour matches the '3' on the card, but it's very translucent, rather than a lot of that colour so closer to the 0-1 really
I opted for the 0-1 reading as the strip shows no sign of colour at all ....... Still very noob, I'm afraid!