In the part when Whistler is giving Blade his serum, Blade is strapped down. Whistler leaves to catch the girl, Blade comes from behind, and Whistler leaves without undoing Blade. So, how did he get out?
If you notice while Blade is beign injected by the serum his arms are able to lift a good distance off the arm rest. They were not put there necessarily to trap him but to keep his arms down. I'm sure that once he was calm he could maneuver his hands to release them himself.