Verify relays soldered onto a circuit board
There should be no issue manually powering those relays to test them, although it looks like they have flyback diodes with them,  So:


Be careful about the polarity you apply since the diodes (the ones labelled "4007" on the board - they'll be 1N4007 diodes) would cause a dead short if connected the wrong way.
The provided flyback diodes would make convenient test points for attaching your power to whilst keeping the board component side up.


Connect the + to the diode's cathode (left in the picture), and the - to the diode's anode (right in the picture) so the diode is reverse biased, and you should hear a click.

Also, you could attach a DMM to the relay's switch terminals set to continuity test, so you can observe a proper connection when it switches.

You can also use the same DMM in diode test mode as a pre-check test to confirm the diodes are functioning correctly.