My DD wouldn’t tolerate a wristband, it would have come straight off, but we had these little rubber holders with a safety pin. We would then place it somewhere discreet that she hopefully wouldn’t notice, like the back of her waistband. Obviously this needs to be replaced daily onto whatever she is wearing.
The problem with burying them in coats or shoes is that these items are too easily removed or changed. My children will often throw their coat off if they are running around even in the dead of winter. And they might go out in their wellies/crocs/sandals rather than their trainers.