These look like gold-plated pads, but it's hard to tell due to the poor quality of the picture.
Gold solders very easily, as does any other metal that will be the surface of a pad on a PC board with about that color. Having no flux is no exuse. Get some. Actually any reasonable solder for electronic purposes will have flux core, so you don't really need anything more for this problem. Still, it's not a bad idea to have some flux around for general use.
By using solder with flux (however you achieve that), it should be easy to solder small wires to the pads. I'd probably use small 30 gauge "wire wrap" wire.
Added:
With the updated picture, I think it's even more likely those are gold-plated pads. Again, gold is very easy to solder to.
Make sure to strip the insulation from the wire only a short way, not more than the diameter of a pad, prefereably a bit less. Be extra careful that the uninsulated part of the wire doesn't extend past the edge of the pad it is soldered to. That prevents it from shorting to other wires or that strip above the top of the pads. This is all quite doable.