If you are using an uncycled filter then there is no reason to move old water over - water is not cycled so all you are doing is putting them in dirty water that the filter has no way of cleaning for them.

What kind of cories are they? A 10 gallon will be a little tight for 6 but certainly doable if set up correctly. Normally I would say to make sure you wait to buy new ones until you are done cycling, but since you will not have another quarantine tank it will be up to you. When (if) you buy more, make sure it is the same species.

Sand is very important due to their barbles. Do not keep them with gravel. Don't fill up a lot of space with decor. Plants are fine as they will help while going through a cycle but avoid any other decor.

Because it will be uncycled, daily partial waterchanges are going to need to be done for a couple months and do not replace the filter media or you will throw away all your growing bacteria colonies.

In the end, it is up to you as to whether or not you want to keep them. You will also have to decide if you want to buy more now from the same shop, before cycling is done, you will have to do larger daily water changes to deal with the higher bioload. If you wait until after cycling before buying more then you will have to either figure out a way to quarantine the new additions or not quarantine which means you risk entering a disease but won't put more fish through the cycling process. It's a tricky situation and only you will be able to figure out what works best for you.

You could also return the cories and keep the 10 gallon on hand to use as a future quarantine tank for any new frogs.