It won't cause the tank to cycle. I remove and replace my filter cartridges every time they get real dirty or had been in a tank with diease. So it won't cause the tank to cycle. Heck I even had to remove my whole filter and replace it with a bigger one because the one I had couldn't filter all the waste and it didn't recycle.
IMHO that is poor advice.
It is commonly accepted wisdom that you should never change filter media all at once if you can help it. The fact that Durbkat got away with it is neither here nor there in terms of what is best practice. There is a very real risk that it would cause your tank to cycle as you are removing the majority of your bacteria.
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The fact that all your fish are dead means that the bacteria in your filter will not be getting the ammonium required to live, and will probably have died already in the the week since the last fish died. I believe therefore that you're looking at a cycle anyway, in which case you may as well replace the filter media.
Don't take this the wrong way, the point of what I'm saying is not to have a go at anyone.
If you lost all of your fish, it may be that you have not treated the whitespot correctly.
Durbkat is correct to assume you will have whitespot in cists all over the place, and if you add more fish now it follows that you will infect them. It might not be the case, but you have to assume it is.
The ideal option for you is to strip the tank and start again. I strongly advise you take this route. Can you do something with the shrimp in the meantime?
If you can't/don't want to do that, then your best way forward is to treat the whitespot according to the instructions available here
http
/www.fishforums.net/index.php?showtopic=7092 or
http
/www.fishforums.net/index.php?showtopic=107610&st=16.
You'll not know for sure if you've been successful, as you'll have no fish to see are healthy. Please don't stick a guinnea fish in there though.
Continue proper treatment for at least a fortnight (replacing any meds you remove when gravel cleaning/treating the water). Some medications are not good for shellfish, so check what you buy.
You will need to cycle again after treatment, so either start with very hardy fish and add more very slowly, or get into a fishless cycle. I'd avoid messing with cycling until you're complete with the whitespot treatment.