Yes and no. Those are constant current drivers, which will automatically vary their output voltage, within the stated range, to achieve the 1200mA / 1000mA current through their load. If you use the 1000mA driver it will work with the led array you have but will be dimmer. I don't know how much dimmer, and I doubt if it's a simple proportional relationship.
If you want to re-use the leds on a battery source then you need to work out how the two sections are originally wired. If they are wired in series then each half is going to work in the 15 to 21 volt range.
If they are wired in parallel then they work in the 30 - 42 volt range. Get the idea ?
Now I'm guessing that the battery source you have in mind would be 12 or 24 volts. No harm would arise from connecting the lower voltage one to a 12 volt battery, or the higher to a 24 volt battery. They will light up to some extent, but I've no idea how much or if it would be useful. If they don't light at all reverse the connections.
Alternatively, if you want a cheap battery powered light in your shed, then 12volt led strip is readily available, e.g. on Amazon.
