It's about 10-15% depending on the year which is still very high imo. More than likely closer to 15% this year.
Every year there's 2-3 good players in the next 30 picks. Here's some of the players who were still available at the 37th selection and who were drafted not more than 30 picks after that selection (37-67 which also include 31st obviously).
2003 : Patrice Bergeron, David Backes, Shea Weber,
2004 : Carl Soderberg, Brandon Dubinsky, Alex Goligoski, David Krejci
2005 : Paul Stastny, Letang
2006 : Lucic, Anisimov, Petry,
2007 : Subban, Wayne Simmonds,
2008 : Josi, Justin Schultz, Stepan, Scandella,
2009 : Silfverberg, Orlov, Tatar, Tyson Barrie, McNabb, Brian Dumoulin
2010 : Toffoli, Justin Faulk, Zucker
2011 : Jenner, Saad, William Karlsson, Nikita Kucherov, Vincent Trocheck
2012 : Severson, McCabe
2013 : Lehkonen, Bertuzzi, Pesce
2014 : Montour, Dvorak
2015 : Carlo, Hintz, Dunn, Rasmus Andersson
2016 : DeBrincat, Girard, Dillon Dube, Hronek, Adam Fox
I think people grossly underrate the chance to land a good player in the 2nd round specially in the early 2nd round. The chances are obviously a lot lower than in the middle of the first round but there's still 2-3 good players there pretty much every year. Again Newhook will have to be more than a 3rd line player for this trade to be considered good by me.