" Doesn't transistors just decrease/increase voltage from one thing to another?"
No.

To use a relay, get a SPDT or DPDT relay, with a coil appropriate for the voltage supplied.

To use a transistor, use any PNP with the appropriate V, I and P ratings.
If the supply is AC, you'll need to rectify and filter this and apply it, through a resistor, to the base. When current is supplied to the base, the collector emitter remains high impedance, when the base voltage drops, the collector emitter 'shorts' (transistor turns on) to activate your load.