And no, you're not being an idiot. If you don't fully understand something, it's better to ask than to try and fail, hurting your fish and wallet. 
Put the used media into your filter with the new one. This way you get both the benefit of the cycled media and you colonize the new one simultaneously. The majority of the bacteria that you're colonizing will be in the filter media, not the water, gravel or anywhere else. So by changing the water, you won't harm the bacterial colony at all. Assuming you properly treat the water before reintroducing.
While we're on the topic of water changes, have you looked into getting a "Python"? Best water changing apparatus ever!
Put the used media into your filter with the new one. This way you get both the benefit of the cycled media and you colonize the new one simultaneously. The majority of the bacteria that you're colonizing will be in the filter media, not the water, gravel or anywhere else. So by changing the water, you won't harm the bacterial colony at all. Assuming you properly treat the water before reintroducing.
While we're on the topic of water changes, have you looked into getting a "Python"? Best water changing apparatus ever!