Tilt Switch and Transistor without Microcontroller

You do want to use a transistor to increase the effective current handled by the switch. The 2N2222 is good to about 800 mA, if it is saturated.

I’ve attached a simple circuit diagram to show how to do that, assuming that the LED array is current limited to 160 mA, as you stated. If the LED supply is 12V, then the switch (and transistor base) current will be about 12 mA, which should be enough to saturate the transistor at 160 mA.

(Note: LTSpice, used for making the schematic, lacks a standard switch symbol).