I'd say definitely not a rex - or even a mini-rex.
What distinguishes a rex rabbit (or it's smaller cousin a mini-rex) is the rex fur. All rabbits have two types of fur, an undercoat and a set of guard hairs which are (except in rexes) much longer. The longer guard hairs lie down flat over the undercoat. That seems to be just what I see in the pictures you posted, especially the second one.
In rex fur the guard hairs and undercoat hairs are the same length, so the fur stands up and is plush like velvet. Once you've felt rex fur, you'll see there's nothing like it.
Also, the same mutation which produced rex fur also causes the whiskers to be short and kinky or curly, not at all the typical long whiskers you'll see on other rabbits. The whiskers in the second picture are definitely not rex whiskers.
For comparison, here's my Natasha, who has black fur much like your Shya, but who is a mini rex:
(Ignore the grey rabbit, Borders, who is of the "stuffed" breed)
Note the plush fur, and nearly no visible whiskers.
