Don't worry about the 17V - the power supply is not well regulated, but in this application it will have no effect on the performance of the solenoid in the door strike. Hook the positive output of the power supply to your solenoid, the other side of the solenoid to your transistor and the ground side of your power supply to the emitter of your transistor and to Arduino Ground. Put a reverse biased diode across the solenoid to protect your transistor.
Don't add complexity where no complexity is needed. Under load the voltage from your power supply will drop - if it drops too low then you need a larger power supply.