It has the high current because it's cold, it only needs a short time to heat up and light up and the majority of circuits can handle very short overcurrent really well because the connections need to heat up before they break. Using a lightbulb for current limiting works pretty well.
I've successfully used incandescent Bulbs in the past. They have barely any resistance when cold, which is the reason why they usually blow up when you turn them on.
For their size, usually I use more than the power the device will use but less than the wires can handle for a while. In your case id get a lamp with a E10 socket, for example 3.5V 0,7W.
Alternatively you can use a PSU with current limiting features.