What pole design hurts thumbs?

My wife fell on her thumb a couple year ago and it took many months to heal.
The orthopedist told her to use poles where the grip wraps around the hand,
rather than the kind with straps, to protect her thumb in the future. The
wrap around kind is no longer available, so I have picked them out of
discard piles whenever I see them.

I also use the wrap arounds because I don't like the straps, and you can
hook them on the chairlifts rather than hold them. Several people have
noticed mine and said they used to like them also, but they are not
available anymore because they can cause thumb injuries.
Well, that is the exact opposite of what her doctor told her. (and she is
sure she isn't confused on what he told her.)

So, which kind is safer for thumbs? I am not going to change either way,
but she should be using the safer ones. Thanks.