Yes, but you will need both + and - at the relay to make it function.
Using this as a diagram (ignore their notes)
https://www.online-led-store.com/med...SPEC01-WEB.jpg
To switch using the negative wire:
Run your + from the power supply directly to the LED strip AND pin 86 on the relay.
Run your - from the power supply to the reed switch AND pin 87 of the relay
Run a wire from the reed switch (the NO or normally open contact) to pin 85 of the relay
Run a wire from pin 30 of the relay to the - on your LED strip.
This way, your reed switch only sees the power needed to switch the relay on and off (not much), while the relay handles the full power that the strip draws.