Wikitree does not allow multiple trees. Wikitree is one big Global tree.
But you are certainly free to add your wifes profile and her ancestors, although please keep in mind that any living persons will have their profiles UNLISTED for privacy reasons. You will be able to see them since you created them, but noone else can see them - except the Admins.
The only reason why she would need access to Wikitree herself is when (or if) she chooses to upload the results of any DNA test she may choose to take.
My spouse also has no interest in doing Genealogy on wikitree, but he was perfectly fine with me adding his name and details and his siblings, parents and all his other ancestors and cousins.
He chooses to not do a DNA test, simply because he knows where he came from.
I did a DNA test to help my mother to finally discover her biological family. She had been fostered out as a baby and was later adopted.