In order to reduce the chances of scoring, you have to keep the players towards the outside of the ice surface. Although it is non contact, you can still use your body to block the opponent's path to a certain degree and prevent him/her from going around you so use it to your advantage. If the player attempts to cut towards the centre of the ice and you are in his/her path, you will not get a penalty, that player is running into you vs you hitting them.
Keep making the player go to the outside while backing up to prevent him/her from going around you. (He/she should always be in front of you if you're skating backwards) Set a "limit" on the ice where you will no longer back up, usually between the hash marks and the crease, discuss this with your goaltender. At that point you stop and poke check. Backing up any more will just screen the goaltender and prevent him/her from stopping the puck. If the player does manage to go around you, he/she won't really have time to get a good shot off or deke the goaltender.
If while backing up you notice the player has a lot more speed than you do, it's time for plan B, turn around and skate forwards forcing him/her to the outside and try and poke the puck off the stick. While skating forward you can really use your body weight to push (not hit) your opponent towards the outside.
If the play is a 2 on 1, you have to play the pass, be less aggressive, place yourself between the two players to block the pass and slowly try and box the puck carrier to the outside. At this point, your job is to stop the pass and prevent the puck carrier from cutting in front of the net. The goaltender is given the shot. If you pass the "set point" go more aggressively on the puck carrier while still blocking the pass.