The good bacteria likes the water to go constantly "through" the surfaces it has attached itself to, as it needs to get regular supply of ammonia and oxygen which is what it feeds on, so the filter media and filter surfaces will have more bacteria grown on them than the substrate or other decorations inside the tank. So it's quite possible that the filter itself inside along with the filter sponges/media all have bacteria attached.
As someone else suggested, I'd either run the two filters forever as an overfiltered tank is almost impossible to suffer any ammonia spikes, mini or maxi which will prevent any sudden issues and disease outbreaks and also a back up in case one filter fails. The higher flow will pickup the decaying organics instead of them hanging around in or on the substrate, so healthier fish too, less risks of sicknesses.
But if you need to remove the internal eventually, treat the external as an uncycled filter. The bacteria won't just decide to travel from one filter the other to check out the new equipment you've bought for it, no matter how long you run the external alongside the internal. 4 weeks is not enough anyway, you may end up with an uncycled filter as you don't know in which filter the bacteria will prefer to grow and in most cases it stays in the original filter. The amount of bacteria in a tank is just the necessary amount to deal with the current bioload so I doubt it much of it will grow in the external since it's already established itself somewhere else. The best way if you intend removing the internal, is to put all it's cycled media into the external filter and to prepare for a mini spike which may or may not happen. Otherwise you may end up with a completely uncycled tank rather than a mini 4 day spike.
If you are afraid that the filter itself inside has bacteria on the surfaces you may lose that way, give the plastics/impeller a good wash outside the tank without touching the media, leave it for a weak or two to allow the loss to grow somewhere else, hopefully in your external, then get all the media out from the internal and put it into the external at once and take out the internal then.
Another way to speed up the process of transfer would be to wash the internal filter sponges inside the tank itself. It will cause no harm to the fish(they love to eat the floating bits and microorganisms that it contains). Then the external filter will pick up the floating gunk and the disturbed bacteria with it, and if you are lucky, a lot of it may settle into the external filter instead. Your water should clear up in no time with two filters gowing so don't worry about the mess. But leave the two filters for as long as possible, 8 weeks the minimum.