So I think that the best solution for me is to use the 5V output pin and try to lower it with a resistance to 3.7V, since the transistor drains 0.7V.
Is this correct?
That will depend on the device. If it consumes a constant current, you have a chance. Otherwise, no.
If you tell us more about this device of yours, we can help you more.
It's just a device to control the global heating control of my house. It is powered by two AA batteries, which I took out and tried to connect my arduino to it, with GND to the - pole, and 3V to the +.