This may sound like a overly simple answer, but try consciously relaxing your arms when snatching without straps. With straps you don't have to worry about gripping the bar as tightly and your arms will generally be more relaxed because of this. Without straps you may be "death gripping" the bar which will cause unnecessary tension in the arms which will slow down the turn over/lockout. Bud Charniga talks about this here:
" For instance, the main reason a lifter is typically able to snatch or clean more weight with straps is because of the less effort and attention to maintain a secure grip.
It is also worth noting that the muscular tension of grasping the bar, especially when it is excessive, has a tendency to "run up the arm." That is to say, muscles other than the actual gripping muscles become involved needlessly. As a result, a "seamless" switch from flexing to extending the arms is met with an "internal resistance" during the instantaneous fixing of the bar in the snatch."