Captains get trusted for how they treat the weakest player on the roster, not the best one.

Everyone is pleasant to the best player, so that tells a team nothing. How the captain speaks to the last person off the bench is the signal, because there is no advantage in it and no audience that matters. The whole group is watching that anyway, and deciding how safe it is to be struggling in front of this person. Leadership is mostly worked out from that.

Whether or not you wear the armband, pick the person having the worst season and warm up with them this week. Say something specific about what they did well. Do it when nobody is near, which is what makes it count.