Hi. Running the old filter in the new tank, with the same fish as before, should instantly cycle the tank. After a few weeks, if the fish loading stays the same, the bacteria loading will be shared by each filter so removing the old filter could result in a mini cycle. Not too much of a problem if you only have two fish. If possible remove half the media from the old filter after a couple of weeks to push the loading onto the new filter and then remove the old filter totally after a further two weeks. Then test daily just to make sure all is well dosing with Prime if ammonia or nitrites rise a little.
This assumes you don't buy more fish.
Personally I would buy a few fish at a time to slowly load the filters and do small (10%) daily water changes until the filters have caught up with the additional loading.
Cory catfish do like to be in groups of 5 or above but you have to weigh up the risk of introducing them a couple at a time and having the first ones in the tank without 'friends' or buying 5/6 and risking a mini cycle. Personally I would buy a small group, monitor the water well and water change little and often until the filters catch up.
Do corys keep the tank clean? Yes they will eat any food that's reached the bottom of the tank,but that's because you're over feeding the tank. Corys really need catfish food as their main feed and it won't hurt if they have the odd bit of left over flake as well. I've got 18 because I think they're great fish, regardless of any clean up benefits.
My philosophy is that when any changes are made to your tank filters, planting, stocking etc then test daily, use Prime if necessary and water change when required.
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