you do not need to solder the bad cap, just leave it, because there is already another cap on the board. It is also 1000uF 10V. We are just troubleshooting the problems now, to identify other areas causing the problems. You can install the new cap when it come. For now, don't need to, just leave it un-installed, vacant.!
Do you understand what I mean, the 2 capacitors are effectively in parallel across a choke. So one down, still not a big problem as far as DC is concerned.