Its okay that your niece feels uncomfortable with this style of clothing, but you have your history of Seven's attire wrong and if I may be so bold your decision not to show her "scary" eps has prejudiced her opinion.
Jeri Ryan did indeed nearly faint from her costume, but it wasn't the cat suit.
It was the Borg suit that constricted her carotid arteries too much in certain positions that caused her to faint.
Meeting Seven in the Borg costume would help your niece focus on her character and would explain certain aspects of her costume after the transformation like the metal on her skull, her arm and the obvious ribbing we see over her abdomen.
The dermoplastic bandages help her in regenerating her tissue, and it helps to see that they are the same color of her first cat suit.
Watching her evolve not over just the first few eps but throughout the season is probably why your wife can accept the character and ignore the catsuit.
Obviously Kate was upset at the idea of anyone coming on board to boost her show's ratings, especially when the someone was so obviously presented in a sexualized manner and I understand that. I don't know what Avery Brooks thought when they brought Worf onto DS9, but I remember an article where the other men on the show laughed that TPTB decided their show needed more testosterone.
Why don't I mind the costume? Because the character they shoved into that costume was a bad ass woman who took no guff from anyone and who was always, ALWAYS projected as a capable intelligent woman.
What's most important about this character's costume, is that her fellow crewmen/women still treated her with respect and when others didn't treat her thus she dealt with it decisively.
That is a lesson your niece might do well to learn.