Thyra hardly ever smiled in photos; she was emotionless and stone-faced, not unlike most of her peers, but certainly not a person who conveyed any particular emotion in her images. As far as being shy, we know that in today's world she would have been considered a bit of a hussy as a teenager, so shyness is not a term I would apply to her.
Victoria Luise, on the other hand, had an utterly and completely genuine smile and demeanor. If by "cat" like you suggest hers was a sly or sinister look, you couldn't be further from reality. She is one of the few royals of her era to have demonstrated pleasing facial expressions in photos...all very kind in appearance and full of sweetness. This is well documented among various people who were graced by her presence.