A lot of the science surrounding sound and trauma responses has to do with frequency and volume but also context. The frequency of a whistle certainly has the potential to induce trauma responses. When used indoors, the volume of a whistle is amplified by reflecting off of walls and floors. Add in the unexpected nature of a whistle blown indoors, and this demonstrates that blowing a whistle for attention in doors is a bad idea.
However, on the playground, the frequency remains the same but the volume decreases due to the increased area for the sound waves to travel. Also, for some, the context of a whistle blown outside is a bit more expected and thus less startling and less likely to induce a trauma response. The danger, of course, is that it could be blown too loudly or too near children - especially children exposed to trauma.
Some practitioners have addressed this by going to a bell. For example, some have used a school bell, cow bell, or old boxing ring style bell. Ringing the bell to conclude recess is a good student job to establish.
My best advice is to be an everyday scientist. Observe as many children you can as the whistle is blown. Key in on students that you fear may be at risk for trauma responses. If upon hearing the whistle, students turn and amble slowly or run to line up - you're probably fine. If you see students, jump, freeze, or wince, then it may be a good idea to move to a bell.