Serial baud rate adjustment without reset?

Yes, something like this

void setup()
{
  Serial.begin(9600);
  Serial.print("press A for high speed mode, any other key to keep 9600");

  while(Serial.available == 0);
  if (Serial.Read() == 'A') Serial.begin(115200);
}

void loop()
{
  Serial.println("Hello world");
  delay(1000);
}