Quoted from JethroP:

The 15,000 uF capacitor you have selected would probably work fine. But if you are going to have to buy a replacement, why not buy what the manufacturer specifies?
This capacitor is not in the high voltage section. It is low voltage. You should be fine with 6,800-12,000 uF, as long as the voltage rating is 25v or higher.
To answer your question, in this particular circuit, nothing detrimental should happen if you use a 15,000 capacitor, but my recommendation would be to use 6,800-12,000. Besides, the lower capacitance would cost less.