The uncle hired the original maids. They could've ratted Hideko out for reward without the risk.

Could be, but either way I don't think its a major plot hole. A minor quibble maybe.
Poorly Lived and Poorly Died, Poorly Buried and No One Cried

I believed it was because Sookee looked more Japanese. The Count even remarks on her fine bone structure for a Korean girl. The original maid was far too Korean to pass off as a Japanese lady to the mental institution.

1st one didnt fit. They wanted someone who would be much better pick.

You're right, it is a plot hole in the movie BUT the book he adapted the movie from did not have this plot hole because of a major change in the script. As much as I love Park Chan Wook's adaptation of "Fingersmith," he did leave out a major plot point/twist.
Book spoiler ahead
In the book, the person who raised Sook Hee, Mrs. Sucksby, played a bigger role, in fact she was the mastermind of the whole operation. The uncle did not have any wives in the original, he took in "Hideko" (Maud) because his sister that died gave birth to a daughter. His sister grew up confined in the mansion, she decided to run away one day, and she got pregnant (not sure if she was already pregnant when she left). The uncle was looking far and wide for her, when she stumbled upon the thieves' shop. She gave birth there and begged Mrs. Sucksby to help her. She did not want her baby to have the same life that she did, stuck in a mansion, living a lonely existence. So the crafty Mrs. Sucksby took the opportunity to give her another baby, and not just any baby. She gave her own daughter to the dying woman (childbirth issues?). So Sue's (Sook Hee) mom is the dead lady, and Maud's (Hideko) is Mrs. Sucksby. As thanks for her kindness, Sue's mom wrote her a promise dividing her fortune between the two babies (they'll get the money when they turned 21 i think). Mrs. Sucksby was consumed by greed and planned the whole scheme, using the count,so she and her real child, Maud, could get all of the money- stealing Sue's half of the fortune. That's why it HAD to be Sook Hee/Sue.