Can I change 1000 uF, 16 V for 1000 uF, 10 V?
The 16V might be for reason. If the actual voltage rail is below 10V it might be fine. If it is over 10V then it is not fine. But capacitors have also other properties than capacitance and voltage. For example ESR. If the old caps were low-ESR caps, and you put standard caps there, it is also not fine. It completely depends on what the original capacitors were doing in the circuit.