I captain a small local roller hockey team and have done for the last few years. We dont play many games and are not in a league but we train every week and get friendlies where we can. the team is made up of a couple of more senior players, a few in their 20's (including myself) and a lot of kids in the 14-17 age range who have between a few months and just over a year of experience of playing hockey.
As captain of such a young team, i've found myself split between trying to get teammates to understand the game and play as a team and helping them improve their individual skills. I am one of the more experienced players on the team and have a better understanding of the game than most so a lot of my time is spent giving advice and encouraging people when trying to learn new aspects of the game. Fortunately the coach of the team gives me the opportunity to run some drills with the skaters in the team most weeks while he works with our goalie (which is appropriate as he has played goal for many years).
One of the main things of importance I have found is developing a sense of timing for how i speak to teammates both on an individual basis and as a team and what approach I take to this (whether to be friendly and encouraging or be harder on them and set them a challenge). I'll use an example that i'm going to bring up in training tomorrow. Most of the players who have been with the team for a while or who have followed the sport for a while understand the importance of communication and make sure they can be heard while we play. However, some of the younger players are literally silent out there and that includes our new keeper (always a bad trait but worse for a keeper). I have taken a more encouraging approach in past weeks to get people talking to each other but it isn't working so when i turn up to training tomorrow, I'm going to raise my voice a bit to everyone on the team. I'm going to make clear from the start that this is not a problem everyone on the team has but that the problem affects every player on the team when we play and that is why i'm including the whole team in my talk. I'm going to explain (once again) why communication is important and then space everyone out around the hall we use and shout out questions and get people talking loud enough so i can hear the answers. I'm going to be a bit harsh on a few people tomorrow but if they are still having problems, hopefully they will understand why i'm annoyed and that i'm trying to help them. If people dont believe that as a captain you are doing something for the best interest of the team then they wont respond as well.
Communication from the teams captain is very important both during training and matches and also away from the rink. You mention NHL captains setting an example on the rink, that much is up to you. You will have to make sure you always push yourself hard and set the right example in situations while playing. Show that you work hard. Show that you want to improve your game. But dont be afraid to make it known that you will help your teammates out if they need advice on anything.
The way you communicate with your team will be up to you, whether you are a very vocal guy, always shouting/congratulating/instructing people or if you are quite but pick your words very carefully. There is no correct way to do this as there are different approaches, the important thing is to make sure that you make the approach you use work for you. If you are a shouty guy, make sure you aren't only shouting when someone makes a mistake. If someone is careless/dangerous/disrespecful, feel free to shout, but if someone does something good, makes a good play, helps someone out, sacrifices their body to make a play, be sure you use your voice to show that it is appreciated and that although you may shout, its a two way thing and it is your teammates efforts that determine if you are happy or angry when you shout.
Hopefully the above is of some use to you, if you want any more info or want anything clarifying, please ask. Hopefully someone with a bit more experience of being a captain in a more competitve environment will reply to your post as that isn't something that i'm overly familiar with. There isn't really any competition for places on my team, we are glad for every player we get and we dont play lots of games so i'm sure someone out there will have more advice on that aspect of captaincy. When we do play games, I try to play hard and play to my strengths and motivate everyone to either step it up or remain calm out there. Like you, i play a more finesse style of hockey so I look to try and make plays happen. My teammates know that is where my abilities are and that if someone is in front of our keeper, chances are i am not strong enough to move them. If i can take a hit to make a play or throw myself in front of a shot, I'll help in that way, but if the team understands everyones abilities and shortcomings then they are able to recognise if there could be a problem during play then they will be able to decide how best to compensate out there. And when a group of players can do that, they can play as a team. And if everyone plays as a team then it makes the job of a captain a little bit easier.