Possibly. I see a lot of people in this thread using the fact that Smith used a different goalie coach in the offseason as a negative towards Schwartz. Just pointing out that this is very common.
As far as Schwartz teaching Smith to staple his hands to his body. I've never seen him teach anything like that. He is constantly teaching goalies to have their hands up and out.
If you want to judge Schwartz's coaching ability, look at the goalie who he likely has had the biggest impact on, Tristan Jarry. He's having a great year and has a .916 sv% with a few of his earlier years pulling that down. .933 sv% this year.
Another thing to consider, in Schwartz's tenure with the team have they ever had a respectable defense? A poor defense will ruin any goalies numbers and confidence.