I would advise you to get close to him by singing to him or just by calling his name and wait until he reacts to it. So he knows you are there. Then pick him (I never used a blanket, I thought it is better if she feels my hands without any layer). While picking him up don't hesitate or be scared, be gentle and sure.
Wait until he calms down on your lap. You can give him his fav food to make him calm or if he is already calm as a reward. Just be careful not to over feed him ^^
And another important tip is putting your t shirt in his cage, at a place where he sleeps, for him to know how you smell.
I hope this helps.