No, if your cane gets caught on something or pulled by something, you risk it yanking your hand and possibly the rest of you. That's a good way to get injured.

Absolutely not! The cane is designed to fall out of your hand if it hits something too hard or gets caught by anything. Putting the strap around your wrist risks injury to your arm or, worse, dragging you into danger by the arm if your cane gets snagged by something. I’ve been seeing this advice showing up in O&M circles and it disturbs me to no end! The strap exists only to hold a folded cane together (I’m still not sure why it’s on non folding canes; possibly to hang it on a coat hook but I don’t know).

No.

Are you working with someone who can show you how to use the cane?

This is definitely Cane use 101. Are you working with an O&M instructor? The band is not meant to go around your wrist or hand at all, unless you want to get seriously injured.

I learned this the hard way (my O&M teacher forced me to). As others have said, the cane is designed to be dropped if you run into a hard object, gets caught in a crack, etc. If you keep it attached to your wrist, you risk major injuries to your wrist and a good chance at falling with your cane. As far as I know, the function of the strap is for keeping folding canes together or for placing the cane into a hook or chair corner (I have mine hanging next to my retired guide dog’s collar and leash).

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Only when I'm standing still and I need the hand free.